Lattice regularization of chiral gauge theories to all orders of perturbation theory

Journal of High Energy Physics

Volumn 4, Issue 6, 2000, Pages 1-25

  Lüscher, Martin ^a,b  

^a CERN   (Switzerland)

^b DESY   (Germany)

Author keywords

Anomalies in Field and String Theories; Gauge Symmetry; Lattice Gauge Field Theories; Renormalization Regulation and Renormalons

Indexed keywords

EID: 7044247870     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/06/028     Document Type: Article

References (69)

1. C. Becchi, A. Rouet and R. Stora, Renormalization of the abelian Higgs-Kibble model, Comm. Math. Phys. 42 (1975) 127; Renormalization of gauge theories, Ann. Phys. (NY) 98 (1976) 287.
2. C. Becchi, A. Rouet and R. Stora, Renormalization of the abelian Higgs-Kibble model, Comm. Math. Phys. 42 (1975) 127; Renormalization of gauge theories, Ann. Phys. (NY) 98 (1976) 287.
3. C. Becchi, Lectures on the renormalization of gauge theories, in Relativity, groups and topology, Les Houches 1983, B.S. DeWitt and R. Stora eds., North-Holland, Amsterdam, 1984.
4. O. Piguet, S.P. Sorella, Algebraic renormalization: perturbative renormalization, symmetries and anomalies, Lecture notes in physics M28, Springer-Verlag, Berlin, 1995.
5. P.A. Grassi, T. Hurth and M. Steinhauser, Practical algebraic renormalization, hep-ph/9907426.
6. F. Jegerlehner, Facts of life with 75, hep-th/0005255.
7. A. Borrelli, L. Maiani, R. Sisto, G.C. Rossi and M. Testa, Yukawa lattice theory and nonperturbative upper bounds to the fermion mass, Phys. Lett. B 221 (1989) 360; Neutrinos on the lattice: the regularization of a chiral gauge theory, Nucl. Phys. B 333 (1990) 335.
8. A. Borrelli, L. Maiani, R. Sisto, G.C. Rossi and M. Testa, Yukawa lattice theory and nonperturbative upper bounds to the fermion mass, Phys. Lett. B 221 (1989) 360; Neutrinos on the lattice: the regularization of a chiral gauge theory, Nucl. Phys. B 333 (1990) 335.
9. M. Testa, The Rome approach to chirality, in Recent developments in non-perturbative quantum field theory, Seoul 1997, Y.M. Cho and M. Virasoro eds., World Scientific, Singapore, 1998.
10. J.L. Alonso, J.L. Cortes and E. Rivas, Weyl fermion functional integral and two-dimensional gauge theories, Int. J. Mod. Phys. A 5 (1990) 2839.
11. J.L. Alonso, P. Boucaud, F. Lesmes and A.J. van der Sijs, A class of chiral fermion models, Nucl. Phys. B 457 (1995) 175 [hep-lat/9507003].
12. W. Bock, M.F.L. Golterman, Y. Shamir, Gauge fixing approach to lattice chiral gauge theories, 1, Nucl. Phys. 63 (Proc. Suppl.) (1998) 147 [hep-lat/9709113]; Gauge fixing approach to lattice chiral gauge theories, 2, Nucl. Phys. 63 (Proc. Suppl.) (1998) 581 [hep-lat/9709115]; Lattice chiral fermions through gauge fixing, Phys. Rev. Lett. 80 (1998) 3444 [hep-lat/9709154]; Chiral fermions on the lattice through gauge fixing: perturbation theory, Phys. Rev. D 58 (1998) 034501 [hep-lat/9801018].
13. W. Bock, M.F.L. Golterman, Y. Shamir, Gauge fixing approach to lattice chiral gauge theories, 1, Nucl. Phys. 63 (Proc. Suppl.) (1998) 147 [hep-lat/9709113]; Gauge fixing approach to lattice chiral gauge theories, 2, Nucl. Phys. 63 (Proc. Suppl.) (1998) 581 [hep-lat/9709115]; Lattice chiral fermions through gauge fixing, Phys. Rev. Lett. 80 (1998) 3444 [hep-lat/9709154]; Chiral fermions on the lattice through gauge fixing: perturbation theory, Phys. Rev. D 58 (1998) 034501 [hep-lat/9801018].
14. W. Bock, M.F.L. Golterman, Y. Shamir, Gauge fixing approach to lattice chiral gauge theories, 1, Nucl. Phys. 63 (Proc. Suppl.) (1998) 147 [hep-lat/9709113]; Gauge fixing approach to lattice chiral gauge theories, 2, Nucl. Phys. 63 (Proc. Suppl.) (1998) 581 [hep-lat/9709115]; Lattice chiral fermions through gauge fixing, Phys. Rev. Lett. 80 (1998) 3444 [hep-lat/9709154]; Chiral fermions on the lattice through gauge fixing: perturbation theory, Phys. Rev. D 58 (1998) 034501 [hep-lat/9801018].
15. W. Bock, M.F.L. Golterman, Y. Shamir, Gauge fixing approach to lattice chiral gauge theories, 1, Nucl. Phys. 63 (Proc. Suppl.) (1998) 147 [hep-lat/9709113]; Gauge fixing approach to lattice chiral gauge theories, 2, Nucl. Phys. 63 (Proc. Suppl.) (1998) 581 [hep-lat/9709115]; Lattice chiral fermions through gauge fixing, Phys. Rev. Lett. 80 (1998) 3444 [hep-lat/9709154]; Chiral fermions on the lattice through gauge fixing: perturbation theory, Phys. Rev. D 58 (1998) 034501 [hep-lat/9801018].
16. W. Bock, K.C. Leung, M. Golterman and Y. Shamir, Abelian and nonabelian lattice chiral gauge theories through gauge fixing, hep-lat/9912025.
17. M. Testa, Some considerations on chiral gauge theories, hep-lat/9912035.
18. P.H. Ginsparg and K.G. Wilson, A remnant of chiral symmetry on the lattice, Phys. Rev. D 25 (1982) 2649.
19. P. Hasenfratz, Prospects for perfect actions, Nucl. Phys. 63 (Proc. Suppl.) (1998) 53 [hep-lat/9709110]; Lattice QCD without tuning, mixing and current renormalization, Nucl. Phys. B 525 (1998) 401 [hep-lat/9802007].
20. P. Hasenfratz, Prospects for perfect actions, Nucl. Phys. 63 (Proc. Suppl.) (1998) 53 [hep-lat/9709110]; Lattice QCD without tuning, mixing and current renormalization, Nucl. Phys. B 525 (1998) 401 [hep-lat/9802007].
21. P. Hasenfratz, V. Laliena and F. Niedermayer, The index theorem in QCD with a finite cut-off, Phys. Lett. B 427 (1998) 125 [hep-lat/9801021].
22. H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022]; More about exactly massless quarks on the lattice, Phys. Lett. B 427 (1998) 353 [hep-lat/9801031].
23. H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022]; More about exactly massless quarks on the lattice, Phys. Lett. B 427 (1998) 353 [hep-lat/9801031].
24. M. Lüscher, Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation, Phys. Lett. B 428 (1998) 342 [hep-lat/9802011].
25. P. Hernández, K. Jansen and M. Lüscher, Locality properties of Neuberger's lattice Dirac operator, Nucl. Phys. B 552 (1999) 363 [hep-lat/9808010].
26. R. Narayanan, Ginsparg- Wilson relation and the overlap formula, Phys. Rev. D 58 (1998) 097501 [hep-lat/9802018].
27. F. Niedermayer, Exact chiral symmetry, topological charge and related topics, Nucl. Phys. 73 (Proc. Suppl.) (1999) 105 [hep-lat/9810026].
28. M. Lüscher, Abelian chiral gauge theories on the lattice with exact gauge invariance, Nucl. Phys. B 549 (1999) 295 [hep-lat/9811032].
29. H. Suzuki, Gauge invariant effective action in abelian chiral gauge theory on the lattice, Prog. Theor. Phys. 101 (1999) 1147 [hep-lat/9901012].
30. M. Lüscher, Weyl fermions on the lattice and the nonabelian gauge anomaly, Nucl. Phys. B 568 (2000) 162 [hep-lat/9904009].
31. M. Lüscher, Chiral gauge theories on the lattice with exact gauge invariance, Nucl. Phys. 83-84 (Proc. Suppl.) (2000) 34 [hep-lat/9909150].
32. M. Lüscher, Topology and the axial anomaly in abelian lattice gauge theories, Nucl. Phys. B 538 (1999) 515 [hep-lat/9808021].
33. T. Fujiwara, H. Suzuki and K. Wu, Axial anomaly in lattice abelian gauge theory in arbitrary dimensions, Phys. Lett. B 463 (1999) 63 [hep-lat/9906016]; Non-commutative differential calculus and the axial anomaly in abelian lattice gauge theories, Nucl. Phys. B 569 (2000) 643 [hep-lat/9906016]; Application of noncommutative differential geometry on lattice to anomaly analysis in abelian lattice gauge theory, hep-lat/9910030.
34. T. Fujiwara, H. Suzuki and K. Wu, Axial anomaly in lattice abelian gauge theory in arbitrary dimensions, Phys. Lett. B 463 (1999) 63 [hep-lat/9906016]; Non-commutative differential calculus and the axial anomaly in abelian lattice gauge theories, Nucl. Phys. B 569 (2000) 643 [hep-lat/9906016]; Application of noncommutative differential geometry on lattice to anomaly analysis in abelian lattice gauge theory, hep-lat/9910030.
35. T. Fujiwara, H. Suzuki and K. Wu, Axial anomaly in lattice abelian gauge theory in arbitrary dimensions, Phys. Lett. B 463 (1999) 63 [hep-lat/9906016]; Non-commutative differential calculus and the axial anomaly in abelian lattice gauge theories, Nucl. Phys. B 569 (2000) 643 [hep-lat/9906016]; Application of noncommutative differential geometry on lattice to anomaly analysis in abelian lattice gauge theory, hep-lat/9910030.
36. H. Suzuki, Anomaly cancellation condition in lattice gauge theory, hep-lat/0002009.
37. Y electroweak theory on the lattice, hep-lat/0005015.
38. R. Stora, Continuum gauge theories, in New developments in quantum field theory and statistical mechanics, Cargèse 1976, M. Lévy and P. Mitter eds., Plenum Press, New York, 1977.
39. R. Stora, Algebraic structure and topological origin of anomalies, in Progress in gauge field theory Cargèse 1983, G. 't Hooft et al. eds., Plenum Press, New York, 1984.
40. B. Zumino, Chiral anomalies and differential geometry, in Relativity, groups and topology, Les Houches 1983, B.S. DeWitt and R. Stora eds., North-Holland, Amsterdam, 1984.
41. L. Baulieu, Algebraic construction of gauge invariant theories, in Particles and fields, Cargèse 1983, M. Lévy et al. eds., Plenum, New York, 1985.
42. L. Baulieu, Anomalies and gauge symmetry, Nucl. Phys. B 241 (1984) 557; Perturbative gauge theories, Phys. Rep. 129 (1985) 1.
43. L. Baulieu, Anomalies and gauge symmetry, Nucl. Phys. B 241 (1984) 557; Perturbative gauge theories, Phys. Rep. 129 (1985) 1.
44. F. Brandt, N. Dragon and M. Kreuzer, All consistent Yang-Mills anomalies, Phys. Lett. B 231 (1989) 263; Completeness and nontriviality of the solutions of the consistency conditions, Nucl. Phys. B 332 (1990) 224; Lie algebra cohomology, Nucl. Phys. B 332 (1990) 250.
45. F. Brandt, N. Dragon and M. Kreuzer, All consistent Yang-Mills anomalies, Phys. Lett. B 231 (1989) 263; Completeness and nontriviality of the solutions of the consistency conditions, Nucl. Phys. B 332 (1990) 224; Lie algebra cohomology, Nucl. Phys. B 332 (1990) 250.
46. F. Brandt, N. Dragon and M. Kreuzer, All consistent Yang-Mills anomalies, Phys. Lett. B 231 (1989) 263; Completeness and nontriviality of the solutions of the consistency conditions, Nucl. Phys. B 332 (1990) 224; Lie algebra cohomology, Nucl. Phys. B 332 (1990) 250.
47. M. Dubois-Violette, M. Henneaux, M. Talon and C.-M. Viallet, Some results on local cohomologies in field theory, Phys. Lett. B 267 (1991) 81; General solution of the consistency equation, Phys. Lett. B 289 (1992) 361 [hep-th/9206106].
48. M. Dubois-Violette, M. Henneaux, M. Talon and C.-M. Viallet, Some results on local cohomologies in field theory, Phys. Lett. B 267 (1991) 81; General solution of the consistency equation, Phys. Lett. B 289 (1992) 361 [hep-th/9206106].
49. L. Alvarez-Gaumé, An introduction to anomalies, in Fundamental problems of gauge field theory, Erice 1985, G. Velo and A. S. Wightman eds., Plenum Press, New York, 1986.
50. R. A. Bertlmann, Anomalies in quantum field theory, Oxford University Press, Oxford, 1996.
51. E. Witten, An SU(2) anomaly, Phys. Lett. B 117 (1982) 324; Global aspects of current algebra, Nucl. Phys. B 223 (1983) 422.
52. E. Witten, An SU(2) anomaly, Phys. Lett. B 117 (1982) 324; Global aspects of current algebra, Nucl. Phys. B 223 (1983) 422.
53. S. Elitzur and V.P. Nair, Nonperturbative anomalies in higher dimensions, Nucl. Phys. B 243 (1984) 205.
54. O. Bär and I. Campos, Global anomalies in chiral gauge theories on the lattice, hep-lat/0001025.
55. M. Lüscher, Selected topics in lattice field theory, in Fields, strings and critical phenomena, Les Houches 1988, E. Brézin and J. Zinn-Justin eds., North-Holland, Amsterdam, 1989.
56. M. Lüscher and P. Weisz, Background field technique and renormalization in lattice gauge theory, Nucl. Phys. B 452 (1995) 213 [hep-lat/9504006]; Computation of the relation between the bare lattice coupling and the MS coupling in SU(N) gauge theories to two loops, Nucl. Phys. B 452 (1995) 234 [hep-lat/9505011].
57. M. Lüscher and P. Weisz, Background field technique and renormalization in lattice gauge theory, Nucl. Phys. B 452 (1995) 213 [hep-lat/9504006]; Computation of the relation between the bare lattice coupling and the MS coupling in SU(N) gauge theories to two loops, Nucl. Phys. B 452 (1995) 234 [hep-lat/9505011].
58. I. Montvay, G. Münster, Quantum fields on a lattice, Cambridge University Press, Cambridge, 1994.
59. H.J. Rothe, Lattice gauge theories: an introduction, 2nd ed. World Scientific, Singapore, 1997.
60. Y. Kikukawa and A. Yamada, Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly, Phys. Lett. B 448 (1999) 265 [hep-lat/9806013].
61. C. Alexandrou, H. Panagopoulos and E. Vicari, Lambda-parameter of lattice QCD with the overlap-Dirac operator, Nucl. Phys. B 571 (2000) 257 [hep-lat/9909158].
62. M. Ishibashi, Y. Kikukawa, T. Noguchi and A. Yamada, One-loop analyses of lattice QCD with the overlap Dirac operator, Nucl. Phys. B 576 (2000) 501 [hep-lat/9911037].
63. C. Alexandrou, E. Follana, H. Panagopoulos and E. Vicari, One-loop renormalization of fermionic currents with the overlap-Dirac operator, hep-lat/0002010.
64. S. Capitani, Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions, hep-lat/0005008.
65. T. Reisz, A power counting theorem for Feynman integrals on the lattice, Comm. Math. Phys. 116 (1988) 81; Renormalization of Feynman integrals on the lattice, Comm. Math. Phys. 117 (1988) 79.
66. T. Reisz, A power counting theorem for Feynman integrals on the lattice, Comm. Math. Phys. 116 (1988) 81; Renormalization of Feynman integrals on the lattice, Comm. Math. Phys. 117 (1988) 79.
67. T. Reisz, Lattice gauge theory: renormalization to all orders in the loop expansion, Nucl. Phys. B 318 (1989) 417.
68. T. Reisz and H.J. Rothe, Renormalization of lattice gauge theories with massless Ginsparg-Wilson fermions, Nucl. Phys. B 575 (2000) 255 [hep-lat/9908013].
69. D.P. Želobenko, Compact Lie groups and their representations, American Mathematical Society, Providence, 1973.