D-particles on T4/ℤn orbifolds and their resolutions

Nuclear Physics B

Volumn 539, Issue 1-2, 1999, Pages 135-165

  Greene, B R ^a   Lazaroiu, C I ^b,c   Yi, Piljin ^b,c  

^a Columbia University ^*  (United States)

^b Department of Obstetrics Gynecology   (United States)

^c Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Compactification; D branes; Gauge theory; Matrix theory; Moduli space; Orbifold

Indexed keywords

EID: 0033601630     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00754-8     Document Type: Article

References (46)

1. [1] P.S. Aspinwall, B.R. Greene and D.R. Morrison, Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory, Nucl. Phys. B 416 (1994) 414; P.S. Aspinwall, B.R. Greene and D.R. Morrison, Multiple mirror manifolds and topology change in string theory, Phys. Lett. B 303 (1993) 249; E. Witten, Phases of N = 2 theories in two dimensions, Nucl. Phys. B 403 (1993) 159.
2. [1] P.S. Aspinwall, B.R. Greene and D.R. Morrison, Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory, Nucl. Phys. B 416 (1994) 414; P.S. Aspinwall, B.R. Greene and D.R. Morrison, Multiple mirror manifolds and topology change in string theory, Phys. Lett. B 303 (1993) 249; E. Witten, Phases of N = 2 theories in two dimensions, Nucl. Phys. B 403 (1993) 159.
3. [1] P.S. Aspinwall, B.R. Greene and D.R. Morrison, Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory, Nucl. Phys. B 416 (1994) 414; P.S. Aspinwall, B.R. Greene and D.R. Morrison, Multiple mirror manifolds and topology change in string theory, Phys. Lett. B 303 (1993) 249; E. Witten, Phases of N = 2 theories in two dimensions, Nucl. Phys. B 403 (1993) 159.
4. [2] B.R. Greene, D.R. Morrison and A. Strominger, Black hole condensation and the unification of string vacua, Nucl. Phys. B 451 (1995) 109.
5. [3] E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys. B 471 (1996) 195.
6. [4] S.H. Shenker, Another length scale in string theory?. hep-th/9509132.
7. [5] M.R. Douglas, D. Kabat, P. Pouliot and S.H. Shenker, D-branes and short distances in string theory, Nucl. Phys. B 485 (1997) 85.
8. [6] E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335.
9. [7] M.R. Douglas, D-branes and Matrix theory in curved space, Nucl. Phys. B (Proc. Suppl.) 68 (1998) 381, hep-th/9707228; M.R. Douglas, D-branes in curved space, hep-th/9703056.
10. [7] M.R. Douglas, D-branes and Matrix theory in curved space, Nucl. Phys. B (Proc. Suppl.) 68 (1998)381, hep-th/9707228; M.R. Douglas, D-branes in curved space, hep-th/9703056.
11. [8] J.A. Harvey and G. Moore, On the algebras of BPS states, hep-th/9609017.
12. [9] K. Hori and Y. Oz, F-theory, T-duality on K3 surfaces and N = 2 supersymmetric gauge theories in four dimensions. Nucl. Phys. B 501 (1997) 97.
13. [10] M. Bershadsky, V. Sadov and C. Vafa, D-branes and topological field theories, Nucl. Phys. B 463 (1996) 420.
14. [11] M.R. Douglas and G. Moore, D-branes, quivers and ALE instantons, hep-th/9603167.
15. [12] C.V. Johnson and R.C. Myers, Aspects of type IIB theory on ALE spaces, Phys. Rev. D 55 (1997) 6382.
16. [13] M.R. Douglas, B.R. Greene and D.R. Morrison, Orbifold resolution by D-branes, Nucl. Phys. B 506 (1997) 84.
17. [14] B.R. Greene, D-brane topology changing transitions, Nucl. Phys. B 525 (1998) 284, hep-th/9711124.
18. [15] M.R. Douglas and B.R. Greene, Metrics on D-brane orbifolds. Adv. Theor. Math. Phys. 1 (1998) 184.
19. [16] T. Muto, D-branes on orbifolds and topology change, Nucl. Phys. B 521 (1998) 183, hep-th/9711090.
20. [17] K. Mohri, D-branes and quotient singularities of Calabi-Yau fourfolds, Nucl. Phys. B 521 (1998) 161, hep-th/9707012.
21. [18] W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283.
22. [19] A. Connes, M.R. Douglas and A. Schwarz, Non-commutative geometry and Matrix theory: compactification on tori, J. High Energy Phys. 02 (1998) 003 hep-th/9711162.
23. [20] I. Satake, The Gauss-Bonnet theorem for V-manifolds, J. Math. Soc. Jpn. 9 (1957) 46 4; T. Kawasaki, The index of elliptic operators over V-manifolds, Nagoya Math. J. 84 (1981) 135.
24. [20] I. Satake, The Gauss-Bonnet theorem for V-manifolds, J. Math. Soc. Jpn. 9 (1957) 46 4; T. Kawasaki, The index of elliptic operators over V-manifolds, Nagoya Math. J. 84 (1981) 135.
25. [21] S. Ramgoolam and D. Waldram, Zero branes on a compact orbifold. J. High Energy Phys. 07 (1998) 009, hep-th/9805191.
26. [22] E.G. Gimon and J. Polchinski, Consistency conditions for orientifolds and D-manifolds, Phys. Rev. D 54 (1996) 1667.
27. [23] M.R. Douglas, Enhanced gauge symmetry in M(atrix) theory, J. High Energy Phys. 07 (1997) 004; D.E. Diaconescu, M.R. Douglas and J. Gomis, Fractional branes and wrapped branes, J. High EnergyPhys. 02 (1998) 013; D. Berenstein, R. Corrado and J. Distler, Aspects of ALE Matrix models and twisted Matrix strings,Phys. Rev. D 58 (1998) 026005, hep-th/9712049.
28. [23] M.R. Douglas, Enhanced gauge symmetry in M(atrix) theory, J. High Energy Phys. 07 (1997) 004; D.E. Diaconescu, M.R. Douglas and J. Gomis, Fractional branes and wrapped branes, J. High Energy Phys. 02 (1998) 013; D. Berenstein, R. Corrado and J. Distler, Aspects of ALE Matrix models and twisted Matrix strings,Phys. Rev. D 58 (1998) 026005, hep-th/9712049.
29. [23] M.R. Douglas, Enhanced gauge symmetry in M(atrix) theory, J. High Energy Phys. 07 (1997) 004; D.E. Diaconescu, M.R. Douglas and J. Gomis, Fractional branes and wrapped branes, J. High EnergyPhys. 02 (1998) 013; D. Berenstein, R. Corrado and J. Distler, Aspects of ALE Matrix models and twisted Matrix strings, Phys. Rev. D 58 (1998) 026005, hep-th/9712049.
30. [24] P.B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom. 28 (1989) 665; P.B. Kronheimer, A Torelli-type theorem for gravitational instantons, J. Diff. Geom. 29 (1989) 685.
31. [24] P.B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom. 28 (1989)665; P.B. Kronheimer, A Torelli-type theorem for gravitational instantons, J. Diff. Geom. 29 (1989) 685.
32. [25] H. Lange, Ch. Birkenhake, Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften 302 (Springer, Berlin, 1992).
33. [26] D. Mumford, Abelian Varieties (Oxford Univ. Press, Oxford, 1970).
34. [27] A. Kapustin and S. Sethi, The Higgs branch of impurity theories, hep-th/9804027.
35. [28] N.J. Hitchin, A. Karlhede, U. Lindström, M. Roček. Hyper-Kähler metrics and supersymmetry, Comm. Math. Phys. 108 (1987) 535.
36. [29] L. Dixon, J.A. Harvey, C. vafa and E. Witten, Strings on orbifold, I, II, Nucl. Phys. B 261 (1985) 678; B 274 (1986) 285.
37. [29] L. Dixon, J.A. Harvey, C. vafa and E. Witten, Strings on orbifold, I, II, Nucl. Phys. B 261 (1985) 678; B 274 (1986) 285.
38. [30] W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete; 3. Folge, Vol. 4 (Springer, Berlin, 1984).
39. [31] S.K. Donaldson and P.B. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs (Clarendon, Oxford, 1990).
40. [32] M. Maruyama, On a compactification of a moduli space of stable vector bundles on a rational surface, Algebraic geometry and commutative algebra, Vol. I, 233, Kinokuniya, Tokyo, 1988; M. Maruyama and G. Trautmann, On compactifications of the moduli space of instantons, Int. J. Math.1 (1990) 431; M. Maruyama and G. Trautmann, Degenerations of instantons, Complex analysis (Wuppertal, 1991)324, Aspects of Math. E 17 (Vieweg, Braunschweig, 1991); M. Maruyama and G. Trautmann, Limits of instantons. Int. J. Math. 3 (1992), no. 2, 213.
41. [32] M. Maruyama, On a compactification of a moduli space of stable vector bundles on a rational surface,Algebraic geometry and commutative algebra, Vol. I, 233, Kinokuniya, Tokyo, 1988; M. Maruyama and G. Trautmann, On compactifications of the moduli space of instantons, Int. J. Math. 1 (1990) 431; M. Maruyama and G. Trautmann, Degenerations of instantons, Complex analysis (Wuppertal, 1991)324, Aspects of Math. E 17 (Vieweg, Braunschweig, 1991); M. Maruyama and G. Trautmann, Limits of instantons. Int. J. Math. 3 (1992), no. 2, 213.
42. [32] M. Maruyama, On a compactification of a moduli space of stable vector bundles on a rational surface,Algebraic geometry and commutative algebra, Vol. I, 233, Kinokuniya, Tokyo, 1988; M. Maruyama and G. Trautmann, On compactifications of the moduli space of instantons, Int. J. Math.1 (1990) 431; M. Maruyama and G. Trautmann, Degenerations of instantons, Complex analysis (Wuppertal, 1991) 324, Aspects of Math. E 17 (Vieweg, Braunschweig, 1991); M. Maruyama and G. Trautmann, Limits of instantons. Int. J. Math. 3 (1992), no. 2, 213.
43. [32] M. Maruyama, On a compactification of a moduli space of stable vector bundles on a rational surface,Algebraic geometry and commutative algebra, Vol. I, 233, Kinokuniya, Tokyo, 1988; M. Maruyama and G. Trautmann, On compactifications of the moduli space of instantons, Int. J. Math.1 (1990) 431; M. Maruyama and G. Trautmann, Degenerations of instantons, Complex analysis (Wuppertal, 1991) 324, Aspects of Math. E 17 (Vieweg, Braunschweig, 1991); M. Maruyama and G. Trautmann, Limits of instantons. Int. J. Math. 3 (1992), no. 2, 213.
44. [32] M. Maruyama, On a compactification of a moduli space of stable vector bundles on a rational surface,Algebraic geometry and commutative algebra, Vol. I, 233, Kinokuniya, Tokyo, 1988; M. Maruyama and G. Trautmann, On compactifications of the moduli space of instantons, Int. J. Math.1 (1990) 431; M. Maruyama and G. Trautmann, Degenerations of instantons, Complex analysis (Wuppertal, 1991)324, Aspects of Math. E 17 (Vieweg, Braunschweig, 1991); M. Maruyama and G. Trautmann, Limits of instantons. Int. J. Math. 3 (1992), no. 2, 213.
45. [33] S. Bando and T. Siu, Stable sheaves and Einstein-Hermitian metrics, Geometry and analysis on complex manifolds, 39 (World Scientific, Singapore, 1994 ).
46. [34] C.I. Lazaroiu, A non-commutative-geometric interpretation of the resolution of equivariant instanton moduli spaces, hep-th/9805132.