Second and third order observables of the two-matrix model

Journal of High Energy Physics

Volumn 7, Issue 11, 2003, Pages 1425-1454

  Bertola, Marco ^a,b  

^a Gina Cody School of Engineering and Computer Science   (Canada)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Integrable Hierarchies; Matrix Models

Indexed keywords

EID: 23044497771     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/11/062     Document Type: Article

References (47)

1. M. Bertola, Free energy of the two-matrix model/dToda τ-function, Nucl. Phys. B 669 (2003) 435 [hep-th/0306184].
2. M.L. Mehta, Random matrices, 2nd edition, Academic Press, New York 1991.
3. P.M. Bleher and A.R. Its, eds., Random matrix models and their applications, MSRI Research Publications 40, Cambridge Univ. Press, Cambridge, 2001.
4. T. Guhr, A. Muller-Groeling and H.A. Weidenmuller, Random matrix theories in quantum physics: common concepts, Phys. Kept. 299 (1998) 189 [cond-mat/9707301].
5. M. Praehofer and H. Spohn, Universal distributions for growth processes in 1 + 1 dimensions and random matrices, Phys. Rev. Lett. 84 (2000) 4882.
6. J.J.M. Verbaarschot, Random matrix model approach to chiral symmetry, Nucl. Phys. 53 (Proc. Suppl.) (1997) 88 [hep-lat/9607086].
7. F. David, Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 (1985) 45.
8. P. Di Francesco, P. Ginsparg and J. Zinn-Justin, 2D gravity and random matrices, Phys. Kept. 254 (1995) 1 [hep-th/9306153].
9. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M-theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043].
10. K. Ueno and K. Takasaki, Toda lattice hierarchy, Adv. Studies Pure Math. 4 (1984) 1.
11. M. Adler and P. Van Moerbeke, String-orthogonal polynomials, string equations and 2-Toda symmetries, Commun. Pure Appl. Math. 50 (1997) 241.
12. M. Adler and P. van Moerbeke, The spectrum of coupled random matrices, Ann. Math. 149 (1999) 921 [hep-th/9907213].
13. M. Bertola, B. Eynard, J. Harnad, Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem, nlin.si/0208002, to appear in Comm. Math. Phys.
14. M. Bertola, B. Eynard, J. Harnad, Duality of spectral curves arising in two-matrix models, Theor. Math. Phys. 134 (2003) 25.
15. M. Bertola, B. Eynard and J. Harnad, Duality, biorthogonal polynomials and multi-matrix models, Commun. Math. Phys. 229 (2002) 73 [nlin.si/0108049].
16. M. Bertola, B. Eynard, mixed correlation functions of the two-matrix model, J. Phys. A 36 (2003) 7733.
17. M. Bertola, Bilinear semi-classical moment functionals and their integral representation, J. App. Theory 121 (2003) 71.
18. B. Eynard, Large N expansion of the 2-matrix model, J. High Energy Phys. 01 (2003) 051.
19. B. Eynard, Large-N expansion of the 2-matrix model, multicut case, math.ph/0307052.
20. N.M. Ercolani and K.T.-R. McLaughlin, presentation at the Montréal 2002 AMS meeting.
21. V.A. Kazakov, Ising model on a dynamical planar random lattice: exact solution, Phys. Lett. A 119 (1986) 140.
22. K. Takasaki, T. Takebe, SDiff(2) Toda equation-hierarchy, τ-function, and symmetries, Lett. Math. Phys. 23 (1991) 205.
23. K. Takasaki, T. Takebe, SDiff(2) KP hierarchy, infinite analysis, part A, B, Kyoto, 1991,
24. Adv. Ser. Math. Phys., 16 World Sci. Publishing, River Edge, NJ 1992, p. 889.
25. I. Krichever, The τ-function of the universal Whitham hierarchy, matrix models and topological field theories, Commun. Pure Appl. Math. 47 (1994) 437.
26. J.M. Daul, V.A. Kazakov and I.K. Kostov, Rational theories of 2D gravity from the two matrix model, Nucl. Phys. B 409 (1993) 311 [hep-th/9303093].
27. P. Wiegmann, A. Zabrodin, Large scale correlations in normal and general non-hermitean matrix ensembles J. Phys. A 36 (2003) 3411.
28. V.A. Kazakov, A. Marshakov, Complex curve of the two matrix model and its τ-function, J. Phys. A 36 (2003) 3107.
29. B. Eynard, Master loop equations, free energy and correlations for the chain of matrices, J. High Energy Phys. 11 (2003) 018 [hep-th/0309036].
30. K. Takasaki, T. Takebe, Integrable hierarchies and dispersionless limit, Rev. Mod. Phys. 7 (1995) 743.
31. I.K. Kostov, I. Krichever, P. Wiegmann, A. Zabrodin, The τ-function for analytic curves, Random matrix models and their applications, Math. Sci. Res. Inst. Publ. 40, Cambridge Univ. Press, Cambridge 2001, p. 285.
32. I. Krichever, A. Marshakov, A. Zabrodin, Integrable structure of the Dirichlet boundary problem in multiply-connected domains, hep-tb/0309010.
33. A. Marshakov, P. Wiegmann, A. Zabrodin, Integrable structure of the Dirichlet boundary problem in two dimensions, Commun. Math. Phys. 227 (2002) 131.
34. [33) P. Wiegmann, A. Zabrodin, Conformal maps and integrable hierarchies, Commun. Math. Phys. 213 (2000) 523.
35. A. Zabrodin, The dispersionless limit of the Hirota equations in some problems of complex analysis, Tear. Mat. Fiz. 129 (2001) 239.
36. L.A. Takhtajan, Free bosons and τ-functions for compact Riemann surfaces and closed smooth Jordan curves. Current correlation functions, Lett. Math. Phys. 56 (2001) 181.
37. K. Takasaki, T. Takebe, Quasi-classical limit of Toda hierarchy and W-infinity symmetries, Lett. Math. Phys. 28 (1993) 165.
38. L-P. Teo, Analytic functions and integrable hierarchies - characterization of tau-functions, Lett. Math. Phys. 64 (2003) 75.
39. A. Harnack, Über die Vieltheilgkeit der ebenen algebraischen Curven, Math. Ann. 10 (1876) 189.
40. A. Kokotov, D. Korotkin, τ-function on Hurwitz spaces, math-ph/0202034.
41. P. Deift, T. Kriecherbauer, K.T.R. McLaughlin, S. Venakides, Z. Zhou, Strong asymptotics of orthogonal polynomials with respect to exponential weights, Commun. Pure Appl. Math. 52 (1999) 1491.
42. H.E. Rauch, Weierstrass points, branch points, and moduli of Riemann surfaces, Commun. Pure Appl. Math. 12 (1959) 543.
43. J.D. Fay, Kernel functions, analytic torsion, and moduli spaces, Memoirs of AMS, 1992, v. 96, n. 464.
44. A. Kokotov, D. Korotkin, On G-function of Fröbenius manifolds related to Hurwitz spaces, math-ph/0306053.
45. J. Ambjørn, J. Jurkiewicz, Yu. M. Makeenko, Multiloop correlators for two-dimensional quantum gravity, Phys. Lett. B 251 (1990) 517.
46. B. Eynard, Correlation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix, J. Phys. A 31 (1998) 8081.
47. B. Eynard, Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices, Nucl. Phys. B 506 (1997) 633.