Improved matrix-model calculation of the N = 2 prepotential

Journal of High Energy Physics

Volumn 8, Issue 4, 2004, Pages 729-750

  Gómez Reino, Marta ^a   Schnitzer, Howard J ^a   Naculich, Stephen G ^b  

^a BRANDEIS UNIVERSITY   (United States)

^b BOWDOIN COLLEGE   (United States)

Author keywords

1 N Expansion; Extended Supersymmetry; Matrix Models; Nonperturbative Effects

Indexed keywords

EID: 23044467888     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2004/04/033     Document Type: Article

References (71)

1. R. Dijkgraaf and C. Vafa, Matrix models, topological strings and supersymmetric gauge theories, Nucl. Phys. B 644 (2002) 3 [hep-th/0206255];
2. On geometry and matrix models, Nud. Phys. B 644 (2002) 21 [hep-th/0207106].
3. R. Dijkgraaf and C. Vafa, A perturbative window into non-perturbative physics, hep-th/0208048.
4. R. Argurio, G. Ferretti and R. Heise, An introduction to supersymmetric gauge theories and matrix models, hep-th/0311066.
5. N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [hep-th/9407087];
6. Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099].
7. R. Dijkgraaf, S. Gukov, V.A. Kazakov and C. Vafa, Perturbative analysis of gauged matrix models, Phys. Rev. D 68 (2003) 045007 [hep-th/0210238].
8. S.G. Naculich, H.J. Schnitzer and N. Wyllard, The N = 2 U(N) gauge theory prepotential and periods from a perturbative matrix model calculation, Nucl. Phys. B 651 (2003) 106 [hep-th/0211123].
9. A. Klemm, M. Marino and S. Theisen, Gravitational corrections in supersymmetric gauge theory and matrix models, J. High Energy Phys. 03 (2003) 051 [hep-th/0211216].
10. S.G. Naculich, H.J. Schnitzer and N. Wyllard, Matrix model approach to the N = 2 U(N) gauge theory with matter in the fundamental representation, J. High Energy Phys. 01 (2003) 015 [hep-th/0211254].
11. S.G. Naculich, H.J. Schnitzer and N. Wyllard, Matrix-model description of N = 2 gauge theories with non-hyperelliptic Seiberg-Witten curves, Nucl. Phys. B 674 (2003) 37 [hep-th/0305263].
12. R. Boels, J. de Boer, R. Duivenvoorden and J. Wijnhout, Nonperturbative superpotentials and compactification to three dimensions, J. High Energy Phys. 03 (2004) 009 [hep-th/0304061];
13. M. Alishahiha and A.E. Mosaffa, On effective superpotentials and compactification to three dimensions, J. High Energy Phys. 05 (2003) 064 [hep-th/0304247];
14. M. Petrini, A. Tomasiello and A. Zaffaroni, On the geometry of matrix models for N = 1, J. High Energy Phys. 08 (2003) 004 [hep-th/0304251];
15. T. J. Hollowood, Critical points of glueball superpotentials and equilibria of integrable systems, J. High Energy Phys. 10 (2003) 051 [hep-th/0305023];
16. M. Matone and L. Mazzucato, Branched matrix models and the scales of supersymmetric gauge theories, J. High Energy Phys. 07 (2003) 015 [hep-th/0305225].
17. C.-h. Ahn and S.-K. Nam, N = 2 supersymmetric SO(N)/Sp(N) gauge theories from matrix model, Phys. Rev. D 67 (2003) 105022 [hep-th/0301203];
18. Y. Ookouchi and Y. Watabiki, Effective superpotentials for SO/Sp with flavor from matrix models, Mod. Phys. Lett. A 18 (2003) 1113 [hep-th/0301226];
19. R. Abbaspur, A. Imaanpur and S. Parvizi, N = 2 SO(N) SYM theory from matrix model, J. High Energy Phys. 07 (2003) 043 [hep-th/0302083].
20. M. Matone, Instantons and recursion relations in N = 2 SUSY gauge theory, Phys. Lett. B 357 (1995) 342 [hep-th/9506102];
21. G. Bonelli and M. Matone, Nonperturbative renormalization group equation and beta function in N = 2 SUSY Yang-Mills, Phys. Rev. Lett. 76 (1996) 4107 [hep-th/9602174];
22. Nonperturbative relations in N = 2 SUSY Yang-Mills and WDVV equation, Phys. Rev. Lett. 77 (1996) 4712 [hep-th/9605090];
23. T. Eguchi and S.-K. Yang, Prepotentials of n = 2 supersymmetric gauge theories and solition equations, Mod. Phys. Lett. A 11 (1996) 131 [hep-th/9510183];
24. J. Sonnenschein, S. Theisen and S. Yankielowicz, On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories, Phys. Lett. B 367 (1996) 145 [hep-th/9510129].
25. E. D'Hoker, I.M. Krichever and D.H. Phong, The renormalization group equation in N = 2 supersymmetric gauge theories, Nucl. Phys. B 494 (1997) 89 [hep-th/9610156].
26. E. D'Hoker, I.M. Krichever and D.H. Phong, Seiberg- Witten theory, symplectic forms and hamiltonian theory of solitons, hep-th/0212313.
27. 2) Yang-Mills theories, J. High Energy Phys. 03 (2003) 043 [hep-th/0301105].
28. A. Klemm, W. Lerche, S. Yankielowicz and S. Theisen, Simple singularities and N = 2 supersymmetric Yang-Mills theory, Phys. Lett. B 344 (1995) 169 [hep-th/9411048];
29. P.C. Argyres and A.E. Earaggi, The vacuum structure and spectrum of N = 2 supersymmetric SU(N) gauge theory, Phys. Rev. Lett. 74 (1995) 3931 [hep-th/9411057];
30. C) gauge theories, Nucl. Phys. B 452 (1995) 283 [hep-th/9505075];
31. P.C. Argyres, M.R. Plesser and A.D. Shapere, The coulomb phase of N = 2 supersymmetric QCD, Phys. Rev. Lett. 75 (1995) 1699 [hep-th/9505100];
32. J.A. Minahan and D. Nemeschansky, Hyperelliptic curves for supersymmetric Yang-Mills, Nucl. Phys. B 464 (1996) 3 [hep-th/9507032];
33. I.M. Krichever and D.H. Phong, On the integrable geometry of soliton equations and N = 2 supersymmetric gauge theories, J. Diff. Geom. 45 (1997) 349 [hep-th/9604199].
34. K. Landsteiner and E. Lopez, New curves from branes, Nucl. Phys. B 516 (1998) 273 [hep-th/9708118].
35. K. Landsteiner, E. Lopez and D.A. Lowe, Supersymmetric gauge theories from branes and orientifold six-planes, J. High Energy Phys. 07 (1998) 011 [hep-th/9805158].
36. C) gauge theories, Nucl. Phys. B 489 (1997) 179 [hep-th/9609041].
37. G. Chan and E. D'Hoker, Instanton recursion relations for the effective prepotential in N = 2 super Yang-Mills, Nucl. Phys. B 564 (2000) 503 [hep-th/9906193].
38. J.D. Edelstein, M. Mariño and J. Mas, Whitham hierarchies, instanton corrections and soft supersymmetry breaking in N = 2 SU(N) super Yang-Mills theory, Nucl. Phys. B 541 (1999) 671 [hep-th/9805172];
39. J.D. Edelstein, M. Gomez-Reino and J. Mas, Instanton corrections in N = 2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets, Nucl. Phys. B 561 (1999) 273 [hep-th/9904087].
40. N.A. Nekrasov, Seiberg- Witten prepotential from instanton counting, hep-th/0206161;
41. Seiberg-Witten prepotential from instanton counting, hep-th/0306211;
42. H. Nakajima and K. Yoshioka, Instanton counting on blowup, 1, math. AG/0306198.
43. R. Flume and R. Poghossian, An algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential, Int. J. Mod. Phys. A 18 (2003) 2541 [hep-th/0208176];
44. U. Bruzzo, F. Fucito, J.F. Morales and A. Tanzini, Multi-instanton calculus and equivariant cohomology, J. High Energy Phys. 05 (2003) 054 [hep-th/0211108].
45. S.G. Naculich, H. Rhedin and H.J. Schnitzer, One-instanton test of a Seiberg- Witten curve from M-theory: the antisymmetric representation of SU(N), Nucl. Phys. B 533 (1998) 275 [hep-th/9804105];
46. I.P. Ennes, S.G. Naculich, H. Rhedin and H. J. Schnitzer, One instanton predictions of a Setberg- Witten curve from M-theory: the symmetric representation of SU(N), Int. J. Mod. Phys. A 14 (1999) 301 [hep-th/9804151].
47. I.P. Ennes, S.G. Naculich, H. Rhedin and H.J. Schnitzer, One-instanton predictions for non-hyperelliptic curves derived from M-theory, Nucl. Phys. B 536 (1998) 245 [hep-th/9806144].
48. I.P. Ennes, S.G. Naculich, H. Rhedin and H.J. Schnitzer, Two antisymmetric hypermultiplets in N = 2 SU(N) gauge theory: Seiberg- Witten curve and M-theory interpretation, Nucl. Phys. B 558 (1999) 41 [hep-th/9904078].
49. A.E. Ksir and S.G. Naculich, Elliptic fibrations and elliptic models, in Topics in algebraic and noncommutative geometry, G.G. Melles et al. eds., American Mathematical Society, Providence, 2003, Contemp. Math. 324 (2003) 155 [hep-th/0203270];
50. P.C. Argyres, R. Maimon and S. Pelland, The M-theory lift of two O6-planes and four d6 branes, J. High Energy Phys. 05 (2002) 008 [hep-th/0204127].
51. A. Klemm, K. Landsteiner, C.I. Lazaroiu and I. Runkel, Constructing gauge theory geometries from matrix models, J. High Energy Phys. 05 (2003) 066 [hep-th/0303032].
52. M. Aganagic, K. Intriligator, C. Vafa and N.P. Warner, The glueball superpotential, hep-th/0304271.
53. F. Cachazo, Notes on supersymmetric Sp(N) theories with an antisymmetric tensor, hep-th/0307063.
54. c) gauge theories with flavors, Phys. Rev. D 69 (2004) 026006 [hep-th/0307190];
55. K. Landsteiner and C.I. Lazaroiu, On Sp(0) factors and orientifolds, hep-th/0310111.
56. K. Intriligator, P. Kraus, A.V. Ryzhov, M. Shigemori and C. Vafa, On low rank classical groups in string theory, gauge theory and matrix models, hep-th/0311181.
57. P. Kraus and M. Shigemori, On the matter of the Dijkgraaf- Vafa conjecture, J. High Energy Phys. 04 (2003) 052 [hep-th/0303104].
58. L.F. Alday and M. Cirafici, Effective superpotentials via Konishi anomaly, J. High Energy Phys. 05 (2003) 041 [hep-th/0304119].
59. P. Kraus, A.V. Ryzhov and M. Shigemori, Loop equations, matrix models and N = 1 supersymmetric gauge theories, J. High Energy Phys. 05 (2003) 059 [hep-th/0304138].
60. P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2-d gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153].
61. G. 't Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461.
62. R. Argurio, V.L. Campos, G. Ferretti and R. Heise, Exact superpotentials for theories with flavors via a matrix integral, Phys. Rev. D 67 (2003) 065005 [hep-th/0210291];
63. H. Ita, H. Nieder and Y. Oz, Perturbative computation of glueball superpotentials for SO(N) ond USp(N), J. High Energy Phys. 01 (2003) 018 [hep-th/0211261];
64. R.A. Janik and N.A. Obers, SO (TV) superpotential, Seiberg-Witten curves and loop equations, Phys. Lett. B 553 (2003) 309 [hep-th/0212069];
65. S.K. Ashok, R. Corrado, N. Halmagyi, K.D. Kennaway and C. Romelsberger, Unoriented strings, loop equations and N = 1 superpotentials from matrix models, Phys. Rev. D 67 (2003) 086004 [hep-th/0211291].
66. R. Gopakumar, N = 1 theories and a geometric master field, J. High Energy Phys. 05 (2003) 033 [hep-th/0211100].
67. S.G. Naculich, H. J. Schnitzer and N. Wyllard, Cubic curves from matrix models and generalized Konishi anomalies, J. High Energy Phys. 08 (2003) 021 [hep-th/0303268].
68. F. Cachazo, N. Seiberg and E. Witten, Chiral rings and phases of supersymmetric gauge theories, J. High Energy Phys. 04 (2003) 018 [hep-th/0303207].
69. R. Casero and E. Trincherini, Phases and geometry of the N = 1 A(2) quiver gauge theory and matrix models, J. High Energy Phys. 09 (2003) 063 [hep-th/0307054].
70. I.P. Ennes, C. Lozano, S.G. Naculich and H.J. Schnitzer, Elliptic models and M-theory, Nucl. Phys. B 576 (2000) 313 [hep-th/9912133].
71. C) gauge theories, Nucl. Phys. B 489 (1997) 211 [hep-th/9609145].