Matrix eigenvalue model: Feynman graph technique for all genera

Journal of High Energy Physics

Volumn 2006, Issue 12, 2006, Pages

  Chekhov, Leonid ^a   Eynard, Bertrand ^b  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b CEA SACLAY   (France)

Author keywords

1 N Expansion; Differential and Algebraic Geometry; Matrix Models

Indexed keywords

EID: 33846138678     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2006/12/026     Document Type: Review

References (37)

1. G. Akemann, Higher genus correlators for the hermitian matrix model with multiple cuts 1996 Nucl. Phys. B 482 403 [hep-th/9606004]
2. J. Ambjørn, L. Chekhov, C.F. Kristjansen and Y. Makeenko, Matrix model calculations beyond the spherical limit 1993 Nucl. Phys. B 404 127 [Erratum ibid. 1995 B449 681] [hep-th/9302014]
3. A.A. Migdal, Loop equations and 1/N expansion 1983 Phys. Rep. 102 199
4. J. Ambjørn, J. Jurkiewicz and Y.M. Makeenko, Multiloop correlators for two-dimensional quantum gravity 1990 Phys. Lett. B 251 517
5. Yu. Makeenko, Loop equations in matrix models and in 2D quantum gravity 1991 Mod.Phys.Lett. (Brief Reviews) A 6 1901
6. M. Bertola, Free energy of the two-matrix model/Dtoda τ-function 2003 Nucl. Phys. B 669 435 [hep-th/0306184]
7. M. Bertola, Second and third order observables of the two-matrix model 2003 J. High Energy Phys. JHEP11(2003)062 [hep-th/0309192]
8. L. Chekhov, Genus one correlation to multi-cut matrix model solutions 2004 Theor. Math. Phys. 141 1640 [hep-th/0401089]
9. L. Chekhov and B. Eynard, Hermitean matrix model free energy: Feynman graph technique for all genera 2006 J. High Energy Phys. JHEP03(2006)014 [hep-th/0504116]
10. R. Kallosh, From BPS to non-BPS black holes canonically [hep-th/0603003]
11. L. Chekhov, A. Marshakov, A. Mironov and D. Vasiliev, DV and WDVV 2003 Phys. Lett. B 562 323 [hep-th/0301071]
12. L. Chekhov, A. Marshakov, A. Mironov and D. Vasiliev, Complex geometry of matrix models [hep-th/0506075]
13. L. Chekhov and A. Mironov, Matrix models vs. Seiberg-Witten/Whitham theories 2003 Phys. Lett. B 552 293 [hep-th/0209085]
14. F. David, Loop equations and nonperturbative effects in two-dimensional quantum gravity 1990 Mod. Phys. Lett. A 5 1019
15. A. Mironov and A. Morozov, On the origin of virasoro constraints in matrix models: lagrangian approach 1990 Phys. Lett. B 252 47
16. J. Ambjørn and Y.M. Makeenko, Properties of loop equations for the hermitean matrix model and for two-dimensional quantum gravity 1990 Mod. Phys. Lett. A 5 1753
17. H. Itoyama and Y. Matsuo, Noncritical virasoro algebra of D<1 matrix model and quantized string field 1991 Phys. Lett. B 255 202
18. R. Dijkgraaf, A. Sinkovics and M. Temurhan, Matrix models and gravitational corrections 2004 Adv. Theor. Math. Phys. 7 1155 [hep-th/0211241]
19. R. Dijkgraaf and C. Vafa, Matrix models, topological strings and supersymmetric gauge theories 2002 Nucl. Phys. B 644 3 [hep-th/0206255]
20. R. Dijkgraaf and C. Vafa, On geometry and matrix models 2002 Nucl. Phys. B 644 21 [hep-th/0207106]
21. R. Dijkgraaf and C. Vafa, A perturbative window into non-perturbative physics [hep-th/0208048]
22. F.J. Dyson, Statistical theory of the energy levels of complex systems. i 1962 J. Math. Phys. 3 140
23. B. Eynard, Topological expansion for the 1-hermitian matrix model correlation functions 2004 J. High Energy Phys. JHEP11(2004)031 [hep-th/0407261]
24. B. Eynard, Large-N expansion of the 2-matrix model 2003 J. High Energy Phys. JHEP01(2003)051 [hep-th/0210047]
25. B. Eynard, Large-N expansion of the 2-matrix model, multicut case [math-ph/0307052]
26. 2 correction to free energy in hermitian two-matrix model 2005 Lett. Math. Phys. 71 199 [hep-th/0401166]
27. B. Eynard, Loop equations for the semiclassical 2-matrix model with hard edges 2005 J. Stat. Mech. (2005) P10006 [math-ph/0504002]
28. B. Eynard and N. Orantin, Mixed correlation functions in the 2-matrix model and the Bethe ansatz 2005 J. High Energy Phys. JHEP08(2005)028 [hep-th/0504029]
29. B. Eynard and N. Orantin, Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula 2005 J. High Energy Phys. JHEP12(2005)034 [math-ph/0504058]
30. H.M. Farkas, I. Kra, Riemann surfaces 2nd edition, Springer Verlag, 1992
31. J.D. Fay, Theta functions on Riemann surfaces Springer Verlag, 1973
32. V.A. Kazakov and A. Marshakov, Complex curve of the two matrix model and its τ-function 2003 J. Phys. A: Math. Gen. 36 3107 [hep-th/0211236]
33. I.K. Kostov, Conformal field theory techniques in random matrix models [hep-th/9907060]
34. I.M. Krichever, The τ-function of the universal whitham hierarchy, matrix models and topological field theories [hep-th/9205110]
35. I. Krichever, M. Mineev-Weinstein, P. Wiegmann, A. Zabrodin, Laplacian growth and Whitham equations of soliton theory [nlin.SI/0311005]
36. P. Wiegmann and A. Zabrodin, Large-N expansion for normal and complex matrix ensembles [hep-th/0309253]
37. P. Wiegmann and A. Zabrodin, Large-N expansion of the 2D Dyson gas 2006 J. Phys. A: Math. Gen. 39 8933 [hep-th/0601009]