Weak-coupling expansion of a chiral gauge theory on a lattice in the overlap formulation

Nuclear Physics B

Volumn 514, Issue 1-2, 1998, Pages 399-418

  Yamada, Atsushi ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

Chiral fermion; Lattice field theory; Renormalizability

Indexed keywords

EID: 0032536632     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00760-8     Document Type: Article

References (59)

1. [1] D.B. Kaplan, Phys. Lett. B 288 (1992) 342.
2. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
3. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
4. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
5. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
6. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
7. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
8. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
9. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
10. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
11. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
12. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
13. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
14. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
15. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
16. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
17. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
18. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
19. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
20. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
21. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
22. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
23. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
24. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
25. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
26. [2] H. Aoki, S. Iso, J. Nishimura and M. Oshikawa, Modern. Phys. Lett. A 9 (1994) 1755; S. Aoki and H. Hirose, Phys. Rev. D 49 (1994) 2604; S. Aoki and Y. Kikukawa, Modern. Phys. Lett. A 8 (1993) 3517; S. Aoki and K. Nagai, Phys. Rev. D 53 (1996) 5058; S. Chandrasekharan, Phys. Rev. D 49 (1994) 1980; M. Creutz and I. Horvath, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 583; M. Creutz, M. Tytgat, C. Rebbi and S. Xue, hep-lat/9612017; J. Distler and S-J. Rey, hep-lat/9305026; V. Furman and Y. Shamir, hep-lat/9405004; M.F.L. Golterman, K. Jansen and D.B. Kaplan, Phys. Lett. B 301 (1993) 219; M.F.L. Golterman, K. Jansen, D.N. Petcher and J. Vink, Phys. Rev. D 49 (1944) 1606; M.F.L. Golterman and Y. Shamir, hep-lat/9409013; A. Hulsebos, C.P. Korthals-Altes and S. Nicolis, hep-th/9406003; K. Jansen, Phys. Lett. B 288 (1992) 348; hep-lat/9410108; K. Jansen and M. Schmaltz, Phys. Lett. B 296 (1992) 374; D. B. Kaplan, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 597; T. Kawano and Y. Kikukawa, Phys. Rev. D 50 (1994) 5365; Y. Kikukawa and S. Miyazaki, Prog. Theor. Phys. 96 (1996) 1189; R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; C.P. Korthals-Altes, S. Nicolis and J. Prades, Phys. Lett. B 316 (1993) 339; R. Narayanan, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95; Y. Shamir, Nucl. Phys. B 406 (1993) 90; B 417 (1993) 167; Phys. Lett. B 305 (357) 1992; Z. Yand, Phys. Lett. B 296 (1992) 151.
27. [3] R. Narayanan and H. Neuberger, Nucl. Phys. B 412 (1994) 574; Phys. Rev. Lett. 71 (1993) 3251; Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95, 587; Nucl. Phys. B 443 (1995) 305.
28. [3] R. Narayanan and H. Neuberger, Nucl. Phys. B 412 (1994) 574; Phys. Rev. Lett. 71 (1993) 3251; Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95, 587; Nucl. Phys. B 443 (1995) 305.
29. [3] R. Narayanan and H. Neuberger, Nucl. Phys. B 412 (1994) 574; Phys. Rev. Lett. 71 (1993) 3251; Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95, 587; Nucl. Phys. B 443 (1995) 305.
30. [3] R. Narayanan and H. Neuberger, Nucl. Phys. B 412 (1994) 574; Phys. Rev. Lett. 71 (1993) 3251; Nucl. Phys. B (Proc. Suppl.) 34 (1994) 95, 587; Nucl. Phys. B 443 (1995) 305.
31. [4] Nielsen and Ninomiya, Nucl. Phys. B 185 (1981) 20; B 195 (1982) 541; B 193 (1981) 173.
32. [4] Nielsen and Ninomiya, Nucl. Phys. B 185 (1981) 20; B 195 (1982) 541; B 193 (1981) 173.
33. [4] Nielsen and Ninomiya, Nucl. Phys. B 185 (1981) 20; B 195 (1982) 541; B 193 (1981) 173.
34. [5] R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; S. Randjbar-Daemi, private communication.
35. [5] R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; S. Randjbar-Daemi, private communication.
36. [6] R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; S. Randjbar-Daemi and J. Strathdee, Phys. Lett. B 348 (1995) 543; Phys. Rev. D 51 (1995) 6619; Nucl. Phys. B 443 (1995) 386; Phys. Lett. B 402 (1997) 134.
37. [6] R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; S. Randjbar-Daemi and J. Strathdee, Phys. Lett. B 348 (1995) 543; Phys. Rev. D 51 (1995) 6619; Nucl. Phys. B 443 (1995) 386; Phys. Lett. B 402 (1997) 134.
38. [6] R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; S. Randjbar-Daemi and J. Strathdee, Phys. Lett. B 348 (1995) 543; Phys. Rev. D 51 (1995) 6619; Nucl. Phys. B 443 (1995) 386; Phys. Lett. B 402 (1997) 134.
39. [6] R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; S. Randjbar-Daemi and J. Strathdee, Phys. Lett. B 348 (1995) 543; Phys. Rev. D 51 (1995) 6619; Nucl. Phys. B 443 (1995) 386; Phys. Lett. B 402 (1997) 134.
40. [6] R. Narayanan and H. Neuberger, Phys. Lett. B 302 (1993) 62; S. Randjbar-Daemi and J. Strathdee, Phys. Lett. B 348 (1995) 543; Phys. Rev. D 51 (1995) 6619; Nucl. Phys. B 443 (1995) 386; Phys. Lett. B 402 (1997) 134.
41. [7] S. Randjbar-Daemi and J. Strathdee, Nucl. Phys. B 461 (1996) 305; Y. Kikukawa, Nucl. Phys. B (Proc. Suppl.) 47 (1996) 599.
42. [7] S. Randjbar-Daemi and J. Strathdee, Nucl. Phys. B 461 (1996) 305; Y. Kikukawa, Nucl. Phys. B (Proc. Suppl.) 47 (1996) 599.
43. [8] S. Aoki and R.B. Levien, Phys. Rev. D 51 (1995) 3790.
44. [9] S. Randjbar-Daemi and J. Strathdee, Nucl. Phys. B 466 (1996) 335.
45. [10] Y. Kikukawa, hep-lat/9705024: hep-lat/9707010.
46. [11] A. Yamada, Phys. Rev. D 57 (1998) 1433.
47. [12] R. Narayanan and H. Neuberger, Phys. Lett. B 348 (1995) 549; Nucl. Phys. B 477 (1996) 521; R. Narayanan, H. Neuberger and P. Vranas, Phys. Lett. B 353 (1995) 507; Y. Kikukawa, R. Narayanan and H. Neuberger, Phys. Lett. B 399 (1997) 105; hep-lat/9705006; S. Aoki, K. Nagai and S.V. Zenkin, hep-lat9705001.
48. [12] R. Narayanan and H. Neuberger, Phys. Lett. B 348 (1995) 549; Nucl. Phys. B 477 (1996) 521; R. Narayanan, H. Neuberger and P. Vranas, Phys. Lett. B 353 (1995) 507; Y. Kikukawa, R. Narayanan and H. Neuberger, Phys. Lett. B 399 (1997) 105; hep-lat/9705006; S. Aoki, K. Nagai and S.V. Zenkin, hep-lat9705001.
49. [12] R. Narayanan and H. Neuberger, Phys. Lett. B 348 (1995) 549; Nucl. Phys. B 477 (1996) 521; R. Narayanan, H. Neuberger and P. Vranas, Phys. Lett. B 353 (1995) 507; Y. Kikukawa, R. Narayanan and H. Neuberger, Phys. Lett. B 399 (1997) 105; hep-lat/9705006; S. Aoki, K. Nagai and S.V. Zenkin, hep-lat9705001.
50. [12] R. Narayanan and H. Neuberger, Phys. Lett. B 348 (1995) 549; Nucl. Phys. B 477 (1996) 521; R. Narayanan, H. Neuberger and P. Vranas, Phys. Lett. B 353 (1995) 507; Y. Kikukawa, R. Narayanan and H. Neuberger, Phys. Lett. B 399 (1997) 105; hep-lat/9705006; S. Aoki, K. Nagai and S.V. Zenkin, hep-lat9705001.
51. [12] R. Narayanan and H. Neuberger, Phys. Lett. B 348 (1995) 549; Nucl. Phys. B 477 (1996) 521; R. Narayanan, H. Neuberger and P. Vranas, Phys. Lett. B 353 (1995) 507; Y. Kikukawa, R. Narayanan and H. Neuberger, Phys. Lett. B 399 (1997) 105; hep-lat/9705006; S. Aoki, K. Nagai and S.V. Zenkin, hep-lat9705001.
52. [13] J. Nishimura, hep-lat/9701013: J. Nishimura and N. Maru, hep-th/9705152; R. Narayanan and J. Nishimura, hep-th/9703109: H. Neuberger, hep-lat/9707022: Y. Kikukawa and H. Neuberger. hep-lat/9707016.
53. [13] J. Nishimura, hep-lat/9701013: J. Nishimura and N. Maru, hep-th/9705152; R. Narayanan and J. Nishimura, hep-th/9703109: H. Neuberger, hep-lat/9707022: Y. Kikukawa and H. Neuberger. hep-lat/9707016.
54. [13] J. Nishimura, hep-lat/9701013: J. Nishimura and N. Maru, hep-th/9705152; R. Narayanan and J. Nishimura, hep-th/9703109: H. Neuberger, hep-lat/9707022: Y. Kikukawa and H. Neuberger. hep-lat/9707016.
55. [13] J. Nishimura, hep-lat/9701013: J. Nishimura and N. Maru, hep-th/9705152; R. Narayanan and J. Nishimura, hep-th/9703109: H. Neuberger, hep-lat/9707022: Y. Kikukawa and H. Neuberger. hep-lat/9707016.
56. [13] J. Nishimura, hep-lat/9701013: J. Nishimura and N. Maru, hep-th/9705152; R. Narayanan and J. Nishimura, hep-th/9703109: H. Neuberger, hep-lat/9707022: Y. Kikukawa and H. Neuberger. hep-lat/9707016.
57. [14] H. Kawai, R. Nakayama and K. Seo, Nucl. Phys. B 189 (1981) 40.
58. [15] N. Kawamoto, Nucl. Phys. B 190[FS3] (1981) 617.
59. [16] L.H. Karsten and J. Smit, Nucl. Phys. B 183 (1981) 103.