The proof of the Dijkgraaf-Vafa conjecture and application to the mass gap and confinement problems

Journal of High Energy Physics

Volumn 2006, Issue 6, 2006, Pages

  Ferrari, Frank ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Confinement; Gauge Symmetry; Nonperturbative Effects; Supersymmetric gauge theory

Indexed keywords

EID: 33745760459     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2006/06/039     Document Type: Article

References (51)

1. R. Dijkgraaf and C. Vafa, Matrix models, topological strings and supersymmetric gauge theories 2002 Nucl. Phys. B 644 3 [hep-th/0206255]
2. R. Dijkgraaf and C. Vafa, On geometry and matrix models 2002 Nucl. Phys. B 644 21 [hep-th/0207106]
3. R. Dijkgraaf and C. Vafa, A perturbative window into non-perturbative physics [hep-th/0208048]
4. G. Veneziano and S. Yankielowicz, An effective lagrangian for the pure N ≤ 1 supersymmetric Yang-Mills theory 1982 Phys. Lett. B 113 231
5. T.R. Taylor, G. Veneziano and S. Yankielowicz, Supersymmetric QCD and its massless limit: an effective lagrangian analysis 1983 Nucl. Phys. B 218 493
6. F. Cachazo, M.R. Douglas, N. Seiberg and E. Witten, Chiral rings and anomalies in supersymmetric gauge theory 2002 J. High Energy Phys. JHEP12(2002)071 [hep-th/0211170]
7. R. Gopakumar and C. Vafa, On the gauge theory/geometry correspondence 1999 Adv. Theor. Math. Phys. 3 1415 [hep-th/9811131]
8. C. Vafa, Superstrings and topological strings at large-N 2001 J. Math. Phys. 42 2798 [hep-th/0008142]
9. F. Cachazo, K.A. Intriligator and C. Vafa, A large-N duality via a geometric transition 2001 Nucl. Phys. B 603 3 [hep-th/0103067]
10. T.R. Taylor and C. Vafa, RR flux on Calabi-Yau and partial supersymmetry breaking 2000 Phys. Lett. B 474 130 [hep-th/9912152]
11. P. Mayr, On supersymmetry breaking in string theory and its realization in brane worlds 2001 Nucl. Phys. B 593 99 [hep-th/0003198]
12. F. Ferrari, Planar diagrams and Calabi-Yau spaces 2004 Adv. Theor. Math. Phys. 7 619 [hep-th/0309151]
13. F. Cachazo and C. Vafa, N ≤ 1 and N ≤ 2 geometry from fluxes [hep-th/0206017]
14. B. Feng, Seiberg duality in matrix model [hep-th/0211202]
15. B. Feng and Y.-H. He, Seiberg duality in matrix models, II 2003 Phys. Lett. B 562 339 [hep-th/0211234]
16. B. Feng, Note on Seiberg duality in matrix model 2003 Phys. Lett. B 572 68 [hep-th/0303144]
17. F. Ferrari, Quantum parameter space and double scaling limits in N ≤ 1 super Yang-Mills theory 2003 Phys. Rev. D 67 085013 [hep-th/0211069]
18. F. Ferrari, Quantum parameter space in super Yang-Mills, II 2003 Phys. Lett. B 557 290 [hep-th/0301157]
19. F. Cachazo, N. Seiberg and E. Witten, Phases of N ≤ 1 supersymmetric gauge theories and matrices 2003 J. High Energy Phys. JHEP02(2003)042 [hep-th/0301006]
20. F. Cachazo, N. Seiberg and E. Witten, Chiral rings and phases of supersymmetric gauge theories 2003 J. High Energy Phys. JHEP04(2003)018 [hep-th/0303207]
21. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting 2004 Adv. Theor. Math. Phys. 7 831 [hep-th/0206161]
22. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting [hep-th/0306211]
23. N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions [hep-th/0306238]
24. N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N ≤ 2 supersymmetric Yang-Mills theory 1994 Nucl. Phys. B 426 19 [hep-th/9407087]
25. N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N ≤ 2 supersymmetric QCD 1994 Nucl. Phys. B 431 484 [hep-th/9408099]
26. A. Kovner and M.A. Shifman, Chirally symmetric phase of supersymmetric gluodynamics 1997 Phys. Rev. D 56 2396 [hep-th/9702174]
27. R. Argurio, V.L. Campos, G. Ferretti and R. Heise, Exact superpotentials for theories with flavors via a matrix integral 2003 Phys. Rev. D 67 065005 [hep-th/0210291]
28. N. Seiberg, Adding fundamental matter to 'chiral rings and anomalies in supersymmetric gauge theory' 2003 J. High Energy Phys. JHEP01(2003)061 [hep-th/0212225]
29. F. Ferrari, Supersymmetric gauge theories, matrix models and geometric transitions Physics Report to appear
30. M. Aganagic, K. Intriligator, C. Vafa and N.P. Warner, The glueball superpotential 2004 Adv. Theor. Math. Phys. 7 1045 [hep-th/0304271]
31. G. 't Hooft, Topology of the gauge condition and new confinement phases in nonabelian gauge theories 1981 Nucl. Phys. B 190 455
32. R. Dijkgraaf, S. Gukov, V.A. Kazakov and C. Vafa, Perturbative analysis of gauged matrix models 2003 Phys. Rev. D 68 045007 [hep-th/0210238]
33. F. Ferrari, On exact superpotentials in confining vacua 2003 Nucl. Phys. B 648 161 [hep-th/0210135]
34. I. Bena and C. Ciocarlie, Exact N ≤ 2 supergravity solutions with polarized branes 2004 Phys. Rev. D 70 086005 [hep-th/0212252]
35. A. Dymarsky and V. Pestun, On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential 2003 Phys. Rev. D 67 125001 [hep-th/0301135]
36. M. Matone and L. Mazzucato, Branched matrix models and the scales of supersymmetric gauge theories 2003 J. High Energy Phys. JHEP07(2003)015 [hep-th/0305225]
37. 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 2003 J. High Energy Phys. JHEP01(2003)015 [hep-th/0211254]
38. R.A. Janik and N.A. Obers, SO(N) superpotential, Seiberg-Witten curves and loop equations 2003 Phys. Lett. B 553 309 [hep-th/0212069]
39. C.H. Ahn and S.K. Nam, N ≤ 2 supersymmetric SO(N)/SP(N) gauge theories from matrix model 2003 Phys. Rev. D 67 105022 [hep-th/0301203]
40. Y. Ookouchi and Y. Watabiki, Effective superpotentials for SO/Sp with flavor from matrix models 2003 Mod. Phys. Lett. A 18 1113 [hep-th/0301226]
41. S.G. Naculich, H.J. Schnitzer and N. Wyllard, Matrix-model description of N ≤ 2 gauge theories with non- hyperelliptic Seiberg-Witten curves 2003 Nucl. Phys. B 674 37 [hep-th/0305263]
42. M. Matone, Instantons and recursion relations in N ≤ 2 SUSY gauge theory 1995 Phys. Lett. B 357 342 [hep-th/9506102]
43. J. Sonnenschein, S. Theisen and S. Yankielowicz, On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories 1996 Phys. Lett. B 367 145 [hep-th/9510129]
44. T. Eguchi and S.K. Yang, Prepotentials of n ≤ 2 supersymmetric gauge theories and soliton equations 1996 Mod. Phys. Lett. A 11 131 [hep-th/9510183]
45. P.S. Howe and P.C. West, Superconformal ward identities and N ≤ 2 Yang-Mills theory 1997 Nucl. Phys. B 486 425 [hep-th/9607239]
46. N. Dorey, V.V. Khoze and M.P. Mattis, Multi-instanton calculus in N ≤ 2 supersymmetric gauge theory, II. Coupling to matter 1996 Phys. Rev. D 54 7832 [hep-th/9607202]
47. N. Dorey, V.V. Khoze and M.P. Mattis, On N ≤ 2 supersymmetric QCD with 4 flavors, 1997 Nucl. Phys. B 492 607 [hep-th/9611016]
48. O. Aharony and S. Yankielowicz, Exact electric-magnetic duality in N ≤ 2 supersymmetric QCD theories, 1996 Nucl. Phys. B 473 93 [hep-th/9601011]
49. N. Dorey, T.J. Hollowood, S. Prem Kumar and A. Sinkovics, Exact superpotentials from matrix models 2002 J. High Energy Phys. JHEP11(2002)039 [hep-th/0209089]
50. N. Dorey, T.J. Hollowood, S. Prem Kumar and A. Sinkovics, Massive vacua of N ≤ 1* theory and S-duality from matrix models 2002 J. High Energy Phys. JHEP11(2002)040 [hep-th/0209099]
51. M.R. Douglas and S.H. Shenker, Dynamics of SU(N) supersymmetric gauge theory, 1995 Nucl. Phys. B 447 271 [hep-th/9503163]