Genus one contribution to free energy in Hermitian two-matrix model

Nuclear Physics B

Volumn 694, Issue 3, 2004, Pages 443-472

  Eynard, B ^a   Kokotov, A ^b   Korotkin, D ^b  

^a CEA SACLAY   (France)

^b Dept of Electrical and Computer Engineering   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4043144459     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2004.06.031     Document Type: Article

References (36)

1. Mehta M.L. Random Matrices second ed. 2001 Academic Press New York
2. Bleher P.M. Its A.R. (Eds.).Random Matrix Models and their Applications MSRI Research Publications vol. 40 2000 Cambridge Univ. Press Cambridge
3. Di Francesco P. Ginzparg P. Zinn-Zustin J. 2D Gravity and Random matrices Phys. Rep. 254 1995 1
4. Guhr T. Mueller-Groeling A. Weidenmuller H.A. Random matrix theories in quantum physics: common concepts Phys. Rep. 299 1998 189
5. Staudacher M. Combinatorial solution of the two-matrix model Phys. Lett. B 305 1993 332-338
6. Daul J.-M. Kazakov V.A. Kostov I.K. Rational theories of 2d gravity from the two-matrix model Nucl. Phys. B 409 1993 311-338
7. Rauch H.E. A transcendental view of the space of algebraic Riemann surfaces Bull. Am. Math. Soc. 71 1965 1-39
8. Ambjorn J. Chekhov L. Kristjansen C.F. Makeenko Yu. Matrix model calculations beyond the spherical limit Nucl. Phys. B 404 1993 127-172
9. Ambjorn J. Chekhov L. Kristjansen C.F. Makeenko Yu. Nucl. Phys. B 449 1995 681
10. Akemann G. Higher genus correlators for the Hermitian matrix model with multiple cuts Nucl. Phys. B 482 1996 403-430
11. Klemm A. Marino M. Theisen S. Gravitational corrections in supersymmetric gauge theory and matrix models JHEP 0303 2003 051
12. Dijkgraaf R. Sinkovics A. Temurhan M. Matrix models and gravitational corrections hep-th/0211241
13. I. Kostov, unpublished notes
14. Chekhov L. Genus one correction to multi-cut matrix model solutions hep-th/0401089
15. Eynard B. Large N expansion of the two-matrix model hep-th/0210047
16. Eynard B. Large N expansion of the two-matrix model, multi-cut case JHEP 0301 2003 051
17. Bertola M. Free energy of the two-matrix model/Toda tau-function Nucl. Phys. B 669 2003 435-461
18. Bertola M. Second and third order observables of the two-matrix model JHEP 0311 2003 062
19. Dubrovin B. Geometry of 2d Topological Field Theories, Integrable Systems and Quantum Groups Lecture Notes in Math. vol. 1620 1996 120-348 Springer Berlin
20. Kokotov A. Korotkin D. Tau-functions on spaces of holomorphic differentials over Riemann surfaces and determinants of Laplacians in flat metrics with conic singularities math.DG/0405042
21. Kokotov A. Korotkin D. Bergmann tau-function on Hurwitz spaces and its applications math-ph/0310008
22. Kokotov A. Korotkin D. Tau-functions on Hurwitz spaces Math. Phys. Anal. Geom. 7 2004 47-96
23. Kazakov V. Marshakov A. Complex curve of the two matrix model and its tau-function J. Phys. A 36 2003 3107-3136
24. Kitaev A. Korotkin D. On solutions of the Schlesinger equations in terms of Θ-functions Int. Math. Res. Notices 17 1998 877-905
25. Dubrovin B. Zhang Y. Bi-Hamiltonian hierarchies in 2D topological field theory at one-loop approximation Commun. Math. Phys. 198 1998 311-361
26. Kokotov A. Korotkin D. On G-function of Frobenius manifolds related to Hurwitz spaces Int. Math. Res. Notices 7 2004 343-360
27. Korotkin D. Solution of matrix Riemann-Hilbert problems with quasi-permutation monodromy matrices Math. Ann. 329 2004 335-364
28. Dijkgraaf R. Vafa C. On geometry and matrix models Nucl. Phys. B 644 2002 21-39
29. Wiegmann P. Zabrodin A. Large N expansion for normal and complex matrix ensembles hep-th/0309253
30. 1,4 and elliptic Gromov-Witten invariants J. Am. Math. Soc. 10 1997 973-998
31. Manin Yu.I. Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces 1999 American Mathematical Society
32. Knizhnik V.G. Multiloop amplitudes in the theory of quantum strings and complex geometry Sov. Phys. Usp. 32 1990 945-971
33. D'Hoker E. Phong D.H. Functional determinants on Mandelstam diagrams Commun. Math. Phys. 124 1989 629-645
34. Sonoda H. Functional determinants on punctured Riemann surfaces and their application to string theory Nucl. Phys. B 284 1987 157-192
35. Zabrodin A. Dispersionless limit of Hirota equations in some problems of complex analysis Theor. Math. Phys. 129 2001 1511-1525
36. Alvarez O. Fermion determinants, chiral symmetry, and the Wess-Zumino anomaly Nucl. Phys. B 238 1984 61-72