The Whitham deformation of the Dijkgraaf-Vafa theory

Journal of High Energy Physics

Volumn 8, Issue 3, 2004, Pages 1673-1705

  Aoyama, Shogo ^a   Masuda, Takahiro ^b  

^a SHIZUOKA UNIVERSITY   (Japan)

^b HOKKAIDO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Integrable Hierarchies; Matrix Models; Nonperturbative Effects; Topological Field Theories

Indexed keywords

EID: 23044479365     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2004/03/072     Document Type: Review

References (38)

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, Nucl. 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. L. Chekhov and A. Mironov, Matrix models vs. Seiberg-Witten/Whitham theories, Phys. Lett. B 552 (2003) 293 [hep-th/0209085].
5. H. Itoyama and A. Morozov, The Dijkgraaf- Vafa prepotential in the context of general Seiberg-Witten theory, Nucl. Phys. B 657 (2003) 53 [hep-th/0211245];
6. Gluino-condensate (CIV-DV) prepotential from its Whitham-time derivatives, Int. J. Mod. Phys. A 18 (2003) 5889 [hep-th/0301136];
7. L. Chekhov, A. Marshakov, A. Mironov and D. Vasiliev, DV and WDVV, Phys. Lett. B 562 (2003) 323 [hep-th/0301071];
8. M. Matone, Seiberg-Witten duality in Dijkgraaf-Vafa theory, Nucl. Phys. B 656 (2003) 78 [hep-th/0212253].
9. 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];
10. Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099].
11. A. Gorsky, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Integrability and Seiberg-Witten exact solution, Phys. Lett. B 355 (1995) 466 [hep-th/9505035];
12. E.J. Martinec and N.P. Warner, Integrable systems and supersymmetric gauge theory, Nucl. Phys. B 459 (1996) 97 [hep-th/9509161];
13. T. Nakatsu and K. Takasaki, Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory, Mod. Phys. Lett. A 11 (1996) 157 [hep-th/9509162];
14. T. Eguchi and S.-K. Yang, Prepotentials of n = 2 supersymmetric gauge theories and soliton equations, Mod. Phys. Lett. A 11 (1996) 131 [hep-th/9510183];
15. A. Marshakov, A. Mironov and A. Morozov, WDVV-like equations in N = 2 SUSY Yang-Mills theory, Phys. Lett. B 389 (1996) 43 [hep-th/9607109];
16. A. Gorsky, A. Marshakov, A. Mironov and A. Morozov, RG equations from Whitham hierarchy, Nucl. Phys. B 527 (1998) 690 [hep-th/9802007].
17. H. Itoyama and A. Morozov, Prepotential and the Seiberg- Witten theory, Nucl. Phys. B 491 (1997) 529 [hep-th/9512161].
18. M. Marino and G.W. Moore, The Donaldson- Witten function for gauge groups of rank larger than one, Commun. Math. Phys. 199 (1998) 25 [hep-th/9802185];
19. M. Marino, The uses of Whitham hierarchies, Prog. Theor. Phys. Suppl. 135 (1999) 29 [hep-th/9905053];
20. A. Losev, N. Nekrasov and S.L. Shatashvili, Issues in topological gauge theory, Nucl. Phys. B 534 (1998) 549 [hep-th/9711108];
21. K. Takasaki, Whitham deformations and tau functions in N = 2 supersymmetric gauge theories, Prog. Theor. Phys. Suppl. 135 (1999) 53 [hep-th/9905224].
22. S. Novikov, S.V. Manakov, L.P. Pitaevskii and V.E. Zakharov, Theory of solitons: the inverse problem method, Plenum Press, New York 1984;
23. A.V. Gurevich and L.P. Pitaevskii, Nonstationary structure of a collisionless shock wave, Sov. Phys. JETP 38 (1974) 291;
24. H. Flaschka, M.G. Forest and D.W. McLaughlin, Multiphase averaging and inverse spectral solution of the Korteweg-de Vries equation, Commun. Pure Appl. Math. 33 (1980) 739;
25. B.A. Dubrovin and S.P. Novikov, Hydrodynamics of weakly deformed soliton lattices. Differential geometry and hamiltonian theoryx, Russian Math. Surveys 44:6 (1989) 35;
26. A.M. Bloch and Y. Kodama, The Whitham equation and shocks in the Toda lattice in Singular limits of dispersive waves, N.M. Ercolani et al eds., Plenum Press, New York 1994.
27. 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];
28. Factorization of Seiberg-Witten curves and compactification to three dimensions, J. High Energy Phys. 03 (2004) 010 [hep-th/0305189];
29. T.J. Hollowood, Critical points of glueball superpotentials and equilibria of integrable systems, J. High Energy Phys. 10 (2003) 051 [hep-th/0305023].
30. Y. Kodama and Gibbons, A method for solving the dispersiomless KP hierarchy, Phys. Lett. A 135 (1989) 167
31. 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];
32. V.A. Kazakov, I.K. Kostov and N.A. Nekrasov, D-particles, matrix integrals and KP hierarchy, Nucl. Phys. B 557 (1999) 413 [hep-th/9810035].
33. R. Dijkgraaf and E. Witten, Mean field theory, topological field theory and multimatrix models, Nucl. Phys. B 342 (1990) 486;
34. R. Dijkgraaf, H. Verlinde and E. Verlinde, Topological strings in D < 1, Nucl. Phys. B 352 (1991) 59.
35. T. Eguchi, Y. Yamada and S.-K. Yang, On the genus expansion in the topological string theory, Rev. Math. Phys. 7 (1995) 279 [hep-th/9405106];
36. B. Dubrovin, Geometry of 2-d topological field theories, hep-th/9407018.
37. S. Aoyama and Y. Kodama, Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy, Commun. Math. Phys. 182 (1996) 185 [hep-th/9505122].
38. N. Dorey, T.J. Hollowood, S. Prem Kumar and A. Sinkovics, Exact superpotentials from matrix models, J. High Energy Phys. 11 (2002) 039 [hep-th/0209089].