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BGWM as second constituent of complex matrix model

A. Alexandrova,b, A. Mironovc,b and A. Morozovb

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[1]
A.S. Alexandrov, A. Mironov and A. Morozov, 2007 Instantons and merons in matrix models, Physica D 235 126 [hep-th/0608228]
CrossRef  Preprint  SPIRES 
[2]
A.S. Alexandrov, A. Mironov and A. Morozov, 2007 M-theory of matrix models, Teor. Mat. Fiz. 150 179 [hep-th/0605171]
CrossRef  Preprint  SPIRES 
[3]
E. Brézin, C. Itzykson, G. Parisi and J.B. Zuber, 1978 Planar diagrams, Commun. Math. Phys. 59 35
CrossRef 
 
D. Bessis, 1979 A new method in the combinatorics of the topological expansion, Commun. Math. Phys. 69 147
CrossRef 
 
D. Bessis, C. Itzykson and J.-B. Zuber, 1980 Quantum field theory techniques in graphical enumeration, Adv. Appl. Math. 1 109
CrossRef 
 
M.-L. Mehta, 1981 A method of integration over matrix variables, Commun. Math. Phys. 79 327
CrossRef 
 
Random matrices, 2nd edition, Academic Press, New York U.S.A. 1991

[4]
A.A. Migdal, 1983 Loop equations and 1/N expansion, Phys. Rept. 102 199
CrossRef 
 
F. David, 1985 Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 45
CrossRef 
 
F. David, 1985 A model of random surfaces with nontrivial critical behavior, Nucl. Phys. B 257 543
CrossRef 
 
J. Ambjørn, B. Durhuus and J. Fröhlich, 1985 Diseases of triangulated random surface models and possible cures, Nucl. Phys. B 257 433
CrossRef 
 
V.A. Kazakov, I.K. Kostov and A.A. Migdal, 1985 Critical properties of randomly triangulated planar random surfaces, Phys. Lett. B 157 295
CrossRef 
 
D.V. Boulatov, V.A. Kazakov, A.A. Migdal and I.K. Kostov, 1986 Possible types of critical behavior and the mean size of dynamically triangulated random surfaces, Phys. Lett. B 174 87
CrossRef 
 
D.V. Boulatov, V.A. Kazakov, A.A. Migdal and I.K. Kostov, 1986 Analytical and numerical study of the model of dynamically triangulated random surfaces, Nucl. Phys. B 275 641
CrossRef 
 
V.A. Kazakov, 1986 Ising model on a dynamical planar random lattice: exact solution, Phys. Lett. A 119 140
CrossRef 
 
V.A. Kazakov, 1989 The appearance of matter fields from quantum fluctuations of 2 D gravity, Mod. Phys. Lett. A 4 2125
CrossRef 
 
L. Alvarez-Gaume, 1990 Random surfaces, statistical mechanics, and string theory, Lausanne lectures, Lausanne Switzerland

 
A. Levin and A. Morozov, 1990 On the foundations of the random lattice approach to quantum gravity, Phys. Lett. B 243 207
CrossRef 
 
P.H. Ginsparg, Matrix models of 2D gravity, [hep-th/9112013]
Preprint  SPIRES 
 
P. Di Francesco and C. Itzykson, 1993 A generating function for fatgraphs Ann. Poincaré 59 117 [hep-th/9212108]
Preprint  SPIRES 
 
J.M. Daul, V.A. Kazakov and I.K. Kostov, 1993 Rational theories of 2D gravity from the two matrix model, Nucl. Phys. B 409 311 [hep-th/9303093]
CrossRef  Preprint  SPIRES 
 
M. Staudacher, 1993 Combinatorial solution of the two matrix model, Phys. Lett. B 305 332 [hep-th/9301038]
CrossRef  Preprint  SPIRES 
 
J. Ambjørn, L. Chekhov, C.F. Kristjansen and Y. Makeenko, 1993 Matrix model calculations beyond the spherical limit, Nucl. Phys. B 404 127 [Erratum ibid B 449 (1995) 681] [hep-th/9302014]
CrossRef  Preprint  SPIRES 
 
P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 1995 2D gravity and random matrices, Phys. Rept. 254 1 [hep-th/9306153]
CrossRef  Preprint  SPIRES 
 
B. Eynard, Large random matrices: eigenvalue distribution, [hep-th/9401165]
Preprint  SPIRES 
 
V.A. Kazakov, M. Staudacher and T. Wynter, 1996 Character expansion methods for matrix models of dually weighted graphs, Commun. Math. Phys. 177 451 [hep-th/9502132]
CrossRef  Preprint  SPIRES 
 
M. Adler, A. Morozov, T. Shiota and P. van Moerbeke, 1996 New matrix model solutions to the Kac-Schwarz problem, Nucl. Phys. (Proc. Suppl.) 49 201 [hep-th/9603066]
CrossRef  Preprint  SPIRES 
 
G. Akemann, 1996 Higher genus correlators for the Hermitian matrix model with multiple cuts, Nucl. Phys. B 482 403 [hep-th/9606004]
CrossRef  Preprint  SPIRES 
 
G. Akemann, P.H. Damgaard, U. Magnea and S. Nishigaki, 1997 Universality of random matrices in the microscopic limit and the Dirac operator spectrum, Nucl. Phys. B 487 721 [hep-th/9609174]
CrossRef  Preprint  SPIRES 
 
G. Akemann, P.H. Damgaard, U. Magnea and S. Nishigaki, 1998 Multicritical microscopic spectral correlators of Hermitian and complex matrices, Nucl. Phys. B 519 682 [hep-th/9712006]
CrossRef  Preprint  SPIRES 
 
T. Guhr, A. Müller-Groeling and H.A. Weidenmuller, 1998 Random matrix theories in quantum physics: common concepts, Phys. Rept. 299 189 [cond-mat/9707301]
CrossRef  Preprint  SPIRES 
 
H.W. Braden, A. Mironov and A. Morozov, 2001 QCD, Wick's theorem for KdV τ-functions and the string equation, Phys. Lett. B 514 293 [hep-th/0105169]
CrossRef  Preprint  SPIRES 
 
B. Eynard, 2000 Random matrices, Saclay Lecture Notes, France, http://www-spht.cea.fr/articles_k2/t01/014/publi.pdf

 
A. Zabrodin, 2003 New applications of non-Hermitian random matrices, Ann. Poincaré 4 S851 [cond-mat/0210331]
CrossRef  Preprint  SPIRES 
 
S.Y. Alexandrov, V.A. Kazakov and D. Kutasov, 2003 Non-perturbative effects in matrix models and D-branes J. High Energy Phys. JHEP09(2003)057 [hep-th/0306177]
IOPscience  Preprint  SPIRES 
 
P.J. Forrester, N.C. Snaith and J.J.M. Verbaarschot, 2003 Developments in random matrix theory, J. Phys. A 36 R1 [cond-mat/0303207]
IOPscience  Preprint  SPIRES 
 
P. Wiegmann and A. Zabrodin, Large-N expansion for normal and complex matrix ensembles, [hep-th/0309253]
Preprint  SPIRES 
 
M. Aganagic, R. Dijkgraaf, A. Klemm, M. Mariño and C. Vafa, 2006 Topological strings and integrable hierarchies, Commun. Math. Phys. 261 451 [hep-th/0312085]
CrossRef  Preprint  SPIRES 
 
R. Teodorescu, E. Bettelheim, O. Agam, A. Zabrodin and P. Wiegmann, 2005 Normal random matrix ensemble as a growth problem: evolution of the spectral curve, Nucl. Phys. B 704 407 [hep-th/0401165]
CrossRef  Preprint  SPIRES 
 
V.A. Kazakov and I.K. Kostov, Instantons in non-critical strings from the two-matrix model, [hep-th/0403152]
Preprint  SPIRES 
 
G. Akemann, Y.V. Fyodorov and G. Vernizzi, 2004 On matrix model partition functions for QCD with chemical potential, Nucl. Phys. B 694 59 [hep-th/0404063]
CrossRef  Preprint  SPIRES 
 
P. Di Francesco, 2 D quantum gravity, matrix models and graph combinatorics, [math-ph/0406013]
Preprint  SPIRES 
 
A. Morozov, Challenges of matrix models, [hep-th/0502010]
Preprint  SPIRES 
 
J. Harnad and A.Y. Orlov, 2007 Fermionic construction of τ functions and random processes, Physica D 235 168 [0704.1157]
CrossRef  Preprint  SPIRES 
 
A. Klemm and P. Sulkowski, 2009 Seiberg-Witten theory and matrix models, Nucl. Phys. B 819 400 [0810.4944]
CrossRef  Preprint  SPIRES 
[5]
F.J. Dyson, 1962 Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3 140
CrossRef 
[6]
A. Morozov, 1992 String theory, what is it?, Sov. Phys. Usp. 35 671
IOPscience 
 
A. Morozov, 1992 Usp. Fiz. Nauk 162 83
CrossRef 
[7]
A. Morozov, 1994 Integrability and matrix models, Phys. Usp. 37 1 [hep-th/9303139]
IOPscience  Preprint  SPIRES 
 
Matrix models as integrable systems, [hep-th/9502091]
Preprint  SPIRES 
 
A. Mironov, 1994 2D gravity and matrix models. 1. 2D gravity, Int. J. Mod. Phys. A 9 4355 [hep-th/9312212]
CrossRef  Preprint  SPIRES 
 
A. Mironov, 2002 Matrix models of two-dimensional gravity Phys. Part. Nucl. 33 537

 
A. Mironov, 2002 Fiz. Elem. Chast. Atom. Yadra 33 1051

[8]
A. Gorsky, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, 1995 Integrability and Seiberg-Witten exact solution, Phys. Lett. B 355 466 [hep-th/9505035]
CrossRef  Preprint  SPIRES 
 
A. Gorsky, A. Marshakov, A. Mironov and A. Morozov, 1998 RG equations from Whitham hierarchy, Nucl. Phys. B 527 690 [hep-th/9802007]
CrossRef  Preprint  SPIRES 
 
A. Marshakov, A. Mironov and A. Morozov, 1996 WDVV-like equations in N=2 SUSY Yang-Mills theory, Phys. Lett. B 389 43 [hep-th/9607109]
CrossRef  Preprint  SPIRES 
 
A. Marshakov, A. Mironov and A. Morozov, 2000 More evidence for the WDVV equations in N=2 SUSY Yang-Mills theories, Int. J. Mod. Phys. A 15 1157 [hep-th/9701123]
CrossRef  Preprint  SPIRES 
 
H.W. Braden and I. Krichever eds., 2000 Integrability: the Seiberg-Witten and Whitham equations, Gordon and Breach, U.S.A.

 
A. Gorsky and A. Mironov, Integrable many-body systems and gauge theories, [hep-th/0011197]
Preprint  SPIRES 
[9]
A. Hurwitz, Uber Riemann'sche Flachen mit gegebenen Verzweigungpunkten (in German), Math. Ann. 39 (1891) 1
CrossRef 
 
Uber die Anzal der Riemann'sche Flachen mit gegebenen Verzweigungpunkten (in German), Math. Ann. 55 1902 53
CrossRef 
 
G. Frobenius, Uber gruppencharakter (in German), Sitzberg. Koniglich Preuss. Akad. Wiss. Berlin, Germany (1896), pg. 985

 
R. Dijkgraaf, 1995 Mirror symmetry and elliptic curves, in The moduli spaces of curves Prog. Math. 129 149, Brikhäuser, U.S.A.

 
R. Vakil, 1997 Enumerative geometry of curves via degeneration methods, Harvard Ph.D. thesis, U.S.A.

 
I. Goulden and D. Jackson, 1997 Transitive factorisations into transpositions and holomorphic mappings on the sphere Proc. Am. Math. Soc. 125 51 [math.CO/9903094]
CrossRef  Preprint 
 
S. Lando and D. Zvonkine, 1999 On multiplicitites of the Lyashko-Looijenga mapping on the discriminant strata, Funct. Anal. Appl. 33 178
CrossRef 
 
Counting ramified coverings and intersection theory on spaces of rational functions. I, [math.AG/0303218]
Preprint 
 
S. Natanzon and V. Turaev, 1999 A compactification of Hurwitz space, Topology 38 889
CrossRef 
 
D. Goulden, D.M. Jackson and A. Vainshtein, 2000 The number of ramifified coverings of the sphere by torus and surfaces of higher genera, Ann. Comb. 4 27, Brikhäuser, U.S.A.
CrossRef 
 
A. Okounkov, 2000 Toda equations for Hurwitz numbers Math. Res. Lett. 7 447

 
A. Givental, Gromov-Witten invariants and quantization of quadratic hamiltonians, [math.AG/0108100]
Preprint 
 
T. Ekedahl, S. Lando, M. Shapiro and A. Vainshtein, 2001 Hurvitz naumbers and intersections on moduli spaces of curves, Invent. Math. 146 297
CrossRef 
 
S. Lando, 2002 Ramified coverings of the two-dimensional sphere and intersection theory in spaces of meromorphic functions on algebraic curves, Russ. Math. Surveys 57 463
IOPscience 
 
A. Alexeevski and S. Natanzon, 2006 Non-commutative extensions of two-dimensional topological field theories and Hurwitz numbers for real algebraic curves, Selecta Math. 12 307 [math.GT/0202164]
CrossRef  Preprint  SPIRES 
 
S. Natanzon, 2006 The normality of some elliptic functional-differential operators of second order, Russ. Math. Surveys 61 185
IOPscience 
 
Disk single Hurwitz numbers, [0804.0242]
Preprint 
 
A. Alexeevski and S. Natanzon, 2008 Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebra of finite groups Am. Math. Soc. Transl. 224 1 [0709.3601]
Preprint  SPIRES 
 
A. Alexeevski and S. Natanzon, 2008 Algebra of two-fold graphs and Hurwitz numbers for seamed surfaces Izvestiya RAN. Seriya fizicheskaya 12 3

 
J. Zhou, Hodge integrals, Hurwitz numbers and symmetric groups, [math.AG/0308024]
Preprint 
 
A. Okounkov and R. Pandharipande, 2006 Gromov-Witten theory, Hurwitz theory, and completed cycles Ann. Math. 163 517 [math.AG/0204305]
CrossRef  Preprint 
 
T. Graber and R. Vakil, 2003 Hodge integrals and Hirwitz numbers via virtual localization Compositio Math. 135 25
CrossRef 
 
M. Kazarian and S. Lando, 2004 Towards the intersection theory of Hurwitz spaces Izv. Ross. Akad. Nauk Ser. Mat. 68 82 [math.AG/0410388]
Preprint 
 
An algebro-geometric proof of Witten's conjecture, [math.AG/0601760]
Preprint 
 
M. Kazarian, KP hierarchy for Hodge integrals, based on the talk at the Moscow Workshop on Combinatorics of moduli spaces, Hurwitz numbers and cluster algebras, Moscow Russia June 2008, [0809.3263]
Preprint 
 
V. Bouchard and M. Mariño, 2008 Hurwitz numbers, matrix models and enumerative geometry, in From Hodge Theory to Integrability and tQFT: tt*-geometry, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, U.S.A. [0709.1458]
Preprint  SPIRES 
 
A. Mironov and A. Morozov, 2009 Virasoro constraints for Kontsevich-Hurwitz partition function J. High Energy Phys. JHEP02(2009)024 [0807.2843]
IOPscience  Preprint  SPIRES 
 
A. Mironov, A. Morozov and S. Natanzon, Complete set of cut-and-join operators in Hurwitz-Kontsevich theory, [0904.4227]
Preprint  SPIRES 
[10]
The standard tau-functions of KP-Toda families are considered in many places, see for example E. Date, M. Jimbo, M. Kashiwara and T. Miwa, 1983 Transformation groups for soliton equations, RIMS Symp. Non-linear integrable systems - classical theory and quantum theory, World Scientific, Singapore

 
V. Kac, 1985 Infinite-dimensional Lie algebras, section 14, Cambridge University Press, Cambridge U.K.

 
V. Kac and M. Wakimoto, 1989 Exceptional hierarchies of soliton equations, Proceedings of Symposia in Pure Mathematics 49 191

[11]
For a concept of generalized τ-functions see A. Mironov, A. Morozov and L. Vinet, 1995 On a c-number quantum τ function, Theor. Math. Phys. 100 890 [hep-th/9312213]
CrossRef  Preprint  SPIRES 
 
For a concept of generalized τ-functions see A. Mironov, A. Morozov and L. Vinet, 1994 Teor. Mat. Fiz. 100 119

 
A. Gerasimov, S. Khoroshkin, D. Lebedev, A. Mironov and A. Morozov, 1995 Generalized Hirota equations and representation theory. 1. The case of SL(2) and SLq(2), Int. J. Mod. Phys. A 10 2589 [hep-th/9405011]
CrossRef  Preprint  SPIRES 
 
S. Kharchev, A. Mironov and A. Morozov, 1995 Non-standard KP evolution and quantum τ-function, Theor. Math. Phys. 104 866 [q-alg/9501013]
CrossRef  Preprint 
 
A. Mironov, Quantum deformations of τ functions, bilinear identities and representation theory, [hep-th/9409190]
Preprint  SPIRES 
 
A. Mironov, 1998 τ-function within group theory approach and its quantization, Theor. Math. Phys. 114 127 [q-alg/9711006]
CrossRef  Preprint 
 
A. Mironov, 1998 Teor. Mat. Fiz. 114 163

[12]
E. Witten, 1990 On the structure of the topological phase of two-dimensional gravity, Nucl. Phys. B 340 281
CrossRef 
[13]
M. Fukuma, H. Kawai and R. Nakayama, 1991 Continuum Schwinger-Dyson equations and universal structures in two-dimensional quantum gravity, Int. J. Mod. Phys. A 6 1385
CrossRef 
[14]
R. Dijkgraaf, E. Verlinde and H. Verlinde, 1991 Topological strings in D < 1, Nucl. Phys. B 352 59
CrossRef 
[15]
A. Gerasimov, A. Marshakov, A. Mironov, A. Morozov and A. Orlov, 1991 Matrix models of 2D gravity and Toda theory, Nucl. Phys. B 357 565
CrossRef 
 
A. Gerasimov et al., 1991 Matrix models as integrable systems: From universality to geometrodynamical principle of string theory, Mod. Phys. Lett. A 6 3079
CrossRef 
[16]
A. Mironov and A. Morozov, 1990 On the origin of Virasoro constraints in matrix models: Lagrangian approach, Phys. Lett. B 252 47
CrossRef 
 
F. David, 1990 Loop equations and nonperturbative effects in two-dimensional quantum gravity, Mod. Phys. Lett. A 5 1019
CrossRef 
 
H. Itoyama and Y. Matsuo, 1991 Noncritical Virasoro algebra of d < 1 matrix model and quantized string field, Phys. Lett. B 255 202
CrossRef 
 
J. Ambjørn and Y.M. Makeenko, 1990 Properties of loop equations for the hermitean matrix model and for two-dimensional quantum gravity, Mod. Phys. Lett. A 5 1753
CrossRef 
[17]
A. Marshakov, A. Mironov and A. Morozov, 1991 Generalized matrix models as conformal field theories: discrete case, Phys. Lett. B 265 99
CrossRef 
 
S. Kharchev, A. Marshakov, A. Mironov, A. Morozov and S. Pakuliak, 1993 Conformal matrix models as an alternative to conventional multimatrix models, Nucl. Phys. B 404 717 [hep-th/9208044]
CrossRef  Preprint  SPIRES 
 
A. Mironov and S. Pakulyak, 1993 On the continuum limit of the conformal matrix models, Theor. Math. Phys. 95 604 [hep-th/9209100]
CrossRef  Preprint  SPIRES 
 
A. Mironov and S. Pakulyak, 1993 Teor. Mat. Fiz. 95 317

 
A. Mironov and S. Pakulyak, 1993 Int. J. Mod. Phys. A 8 3107
CrossRef 
[18]
A. Marshakov, A. Mironov and A. Morozov, 1992 On equivalence of topological and quantum 2D gravity, Phys. Lett. B 274 280 [hep-th/9201011]
CrossRef  Preprint  SPIRES 
[19]
A. Marshakov, A. Mironov and A. Morozov, 1992 From Virasoro constraints in Kontsevich's model to W constraints in two matrix model, Mod. Phys. Lett. A 7 1345 [hep-th/9201010]
CrossRef  Preprint  SPIRES 
[20]
A. Mironov, A. Morozov and G.W. Semenoff, 1996 Unitary matrix integrals in the framework of generalized Kontsevich model. 1. Brezin-Gross-Witten model, Int. J. Mod. Phys. A 11 5031 [hep-th/9404005]
CrossRef  Preprint  SPIRES 
[21]
A. Morozov and S. Shakirov, 2009 Generation of matrix models by &hatW;-operators J. High Energy Phys. JHEP04(2009)064 [0902.2627]
IOPscience  Preprint  SPIRES 
[22]
M. Kontsevich, 1991 Intersection theory on the moduli space of curves, Funct. Anal. Appl. 25 123
CrossRef 
 
M. Kontsevich, 1991 Funkt. Anal. Pril. 25 50
CrossRef 
 
M. Kontsevich, 1992 Intersection theory on the moduli space of curves and the matrix Airy function, Commun. Math. Phys. 147 1
CrossRef 
[23]
S. Kharchev, A. Marshakov, A. Mironov, A. Morozov and A. Zabrodin, 1992 Unification of all string models with C < 1, Phys. Lett. B 275 311 [hep-th/9111037]
CrossRef  Preprint  SPIRES 
 
S. Kharchev, A. Marshakov, A. Mironov, A. Morozov and A. Zabrodin, 1992 Towards unified theory of 2D gravity, Nucl. Phys. B 380 181 [hep-th/9201013]
CrossRef  Preprint  SPIRES 
[24]
S. Kharchev, A. Marshakov, A. Mironov and A. Morozov, 1993 Generalized Kontsevich model versus Toda hierarchy and discrete matrix models, Nucl. Phys. B 397 339 [hep-th/9203043]
CrossRef  Preprint  SPIRES 
[25]
P. Di Francesco, C. Itzykson and J.B. Zuber, 1993 Polynomial averages in the Kontsevich model, Commun. Math. Phys. 151 193 [hep-th/9206090]
CrossRef  Preprint  SPIRES 
[26]
A.S. Alexandrov, A. Mironov and A. Morozov, 2004 Partition functions of matrix models as the first special functions of string theory. I: finite size Hermitean 1-matrix model, Int. J. Mod. Phys. A 19 4127 [hep-th/0310113]
CrossRef  Preprint  SPIRES 
 
A.S. Alexandrov, A. Mironov and A. Morozov, 2005 Teor. Mat. Fiz. 142 419
CrossRef 
 
A.S. Alexandrov, A. Mironov, A. Morozov and P. Putrov, 2009 Partition functions of matrix models as the first special functions of string theory. II. Kontsevich model, Int. J. Mod. Phys. A 24 4939 [0811.2825]
CrossRef  Preprint  SPIRES 
 
These papers collect results from a vast variety of other works, see reference lists therein

[27]
A. Givental, Semisimple Frobenius structures at higher genus, [math.AG/0008067]
Preprint 
[28]
B. Eynard, 2004 Topological expansion for the 1-hermitian matrix model correlation functions J. High Energy Phys. JHEP11(2004)031 [hep-th/0407261]
IOPscience  Preprint  SPIRES 
 
B. Eynard, 2003 Large-N expansion of the 2-matrix model J. High Energy Phys. JHEP01(2003)051 [hep-th/0210047]
IOPscience  Preprint  SPIRES 
 
B. Eynard, 2003 Master loop equations, free energy and correlations for the chain of matrices J. High Energy Phys. JHEP11(2003)018 [hep-th/0309036]
IOPscience  Preprint  SPIRES 
 
B. Eynard and N. Orantin, 2005 Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula J. High Energy Phys. JHEP12(2005)034 [math-ph/0504058]
IOPscience  Preprint  SPIRES 
 
L. Chekhov and B. Eynard, 2006 Hermitean matrix model free energy: Feynman graph technique for all genera J. High Energy Phys. JHEP03(2006)014 [hep-th/0504116]
IOPscience  Preprint  SPIRES 
 
L. Chekhov and B. Eynard, 2006 Matrix eigenvalue model: Feynman graph technique for all genera J. High Energy Phys. JHEP12(2006)026 [math-ph/0604014]
IOPscience  Preprint  SPIRES 
 
B. Eynard, M. Mariño and N. Orantin, 2007 Holomorphic anomaly and matrix models J. High Energy Phys. JHEP06(2007)058 [hep-th/0702110]
IOPscience  Preprint  SPIRES 
 
N. Orantin, Gaussian matrix model in an external field and non-intersecting Brownian motions, [0803.0705]
Preprint  SPIRES 
 
Symplectic invariants, Virasoro constraints and Givental decomposition, [0808.0635]
Preprint  SPIRES 
[29]
I.M. Krichever and S.P. Novikov, 1987 Algebras of Virasoro type, Riemann surfaces and the structure of soliton theory Funct. Anal. Appl. 21 126
CrossRef 
 
I.M. Krichever and S.P. Novikov, 1987 Funkt. Anal. Pril. 21 47

 
I.M. Krichever and S.P. Novikov, 1988 Virasoro-Gelfand-Fuks type algebras, Riemann surfaces, operator's theory of closed strings, J. Geom. Phys. 5 631
CrossRef 
 
I.M. Krichever and S.P. Novikov, 1987 Virasoro-type algebras, Riemann surfaces and strings in Minkowsky space, Funct. Anal. Appl. 21 294
CrossRef 
 
I.M. Krichever and S.P. Novikov, 1989 Algebras of Virasoro type, the energy-momentum tensor, and operator expansions on Riemann surfaces, Funct. Anal. Appl. 23 19
CrossRef 
[30]
T. Morris, 1991 Checkered surfaces and complex matrices, Nucl. Phys. B 356 703
CrossRef 
 
Y. Makeenko, 1990 The complex matrix model and two-dimensional quantum gravity Pisma Zh. Eksp. Teor. Fiz. 52 885

 
Y. Makeenko, 1990 JETP Lett. 52 259

 
A. Anderson, R.C. Myers and V. Periwal, 1991 Complex random surfaces, Phys. Lett. B 254 89
CrossRef 
 
Y. Makeenko, A. Marshakov, A. Mironov and A. Morozov, 1991 Continuum versus discrete Virasoro in one matrix models, Nucl. Phys. B 356 574
CrossRef 
[31]
J. Ambjørn, C.F. Kristjansen and Y.M. Makeenko, 1992 Higher genus correlators for the complex matrix model, Mod. Phys. Lett. A 7 3187 [hep-th/9207020]
CrossRef  Preprint  SPIRES 
[32]
E. Brezin and D. Gross, 1980 The external field problem in the large N limit of QCD, Phys. Lett. B 97 120
CrossRef 
 
D. Gross and E. Witten, 1980 Possible third-order phase transition in the large-N lattice gauge theory, Phys. Rev. D 21 446
CrossRef 
[33]
D. Gross and M. Newman, 1991 Unitary and hermitian matrices in an external field, Phys. Lett. B 266 291
CrossRef 
[34]
K.G. Wilson, 1974 Confinement of quarks, Phys. Rev. D 10 2445
CrossRef 
 
A. Polyakov, 1987 Gauge fields and strings,

 
V.A. Kazakov and A.A. Migdal, 1993 Induced QCD at large-N, Nucl. Phys. B 397 214 [hep-th/9206015]
CrossRef  Preprint  SPIRES 
 
I.I. Kogan, A. Morozov, G.W. Semenoff and N. Weiss, 1993 Area law and continuum limit in 'induced QCD', Nucl. Phys. B 395 547 [hep-th/9208012]
CrossRef  Preprint  SPIRES 
 
I.I. Kogan, A. Morozov, G.W. Semenoff and N. Weiss, 1993 Continuum limits of 'induced QCD': lessons of the Gaussian model at D=1 and beyond, Int. J. Mod. Phys. A 8 1411 [hep-th/9208054]
CrossRef  Preprint  SPIRES 
 
A. Mironov, A. Morozov and T.N. Tomaras, 2005 On the need for phenomenological theory of P-vortices or does spaghetti confinement pattern admit condensed-matter analogies?, J. Exp. Theor. Phys. 101 331 [hep-th/0503212]
CrossRef  Preprint  SPIRES 
[35]
Harish-Chandra, 1957 Differential operators on a semisimple Lie algebra Am. J. Math. 79 87
CrossRef 
 
C. Itzykson and J.B. Zuber, 1980 The planar approximation. 2, J. Math. Phys. 21 411
CrossRef 
 
J. Duistermaat and G. Heckman, 1982 On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 259
CrossRef 
 
A. Hietamaki, A.Y. Morozov, A.J. Niemi and K. Palo, 1991 Geometry of N=1/2 supersymmetry and the Atiyah-Singer index theorem, Phys. Lett. B 263 417
CrossRef 
 
A.Y. Morozov, A. Niemi and K. Palo, 1992 Supersymplectic geometry of supersymmetric quantum field theories, Nucl. Phys. B 377 295
CrossRef 
[36]
M.J. Bowick, A. Morozov and D. Shevitz, 1991 Reduced unitary matrix models and the hierarchy of τ functions, Nucl. Phys. B 354 496
CrossRef 
[37]
A. Morozov, 1992 Pair correlator in the Itzykson-Zuber integral, Mod. Phys. Lett. A 7 3503 [hep-th/9209074]
CrossRef  Preprint  SPIRES 
 
S.L. Shatashvili, 1993 Correlation functions in the Itzykson-Zuber model, Commun. Math. Phys. 154 421 [hep-th/9209083]
CrossRef  Preprint  SPIRES 
 
B. Eynard, A short note about Morozov's formula, [math-ph/0406063]
Preprint  SPIRES 
 
A.P. Ferrer, B. Eynard, P. Di Francesco and J.B. Zuber, 2009 Correlation functions of Harish-Chandra integrals over the orthogonal and the symplectic groups, J. Stat. Phys. 129 885 [math-ph/0610049]
CrossRef  Preprint  SPIRES 
 
M. Bergere and B. Eynard, 2009 Some properties of angular integrals, J. Phys. A 42 265201 [0805.4482]
IOPscience  Preprint  SPIRES 
[38]
S. Kharchev and A. Mironov, 1992 Integrable structures of unitary matrix models, Int. J. Mod. Phys. A 7 4803
CrossRef 
[39]
S. Kharchev, A. Marshakov, A. Mironov and A. Morozov, 1995 Generalized Kazakov-Migdal-Kontsevich model: group theory aspects, Int. J. Mod. Phys. A 10 2015 [hep-th/9312210]
CrossRef  Preprint  SPIRES 
[40]
S. Kharchev, A. Marshakov, A. Mironov, A. Orlov and A. Zabrodin, 1991 Matrix models among integrable theories: forced hierarchies and operator formalism, Nucl. Phys. B 366 569
CrossRef 
[41]
G. Segal and G. Wilson, 1985 Loop groups and equations of KdV type, Inst. Hautes Etudes Sci. Publ. Math. 61 5
CrossRef 
 
D. Friedan and S.H. Shenker, 1986 The integrable analytic geometry of quantum string, Phys. Lett. B 175 287
CrossRef 
 
D. Friedan and S.H. Shenker, 1987 The analytic geometry of two-dimensional conformal field theory, Nucl. Phys. B 281 509
CrossRef 
 
N. Ishibashi, Y. Matsuo and H. Ooguri, 1987 Soliton equations and free fermions on Riemann surfaces, Mod. Phys. Lett. A 2 119
CrossRef 
 
L. Alvarez-Gaume, C. Gomez and C. Reina, 1987 Loop groups, Grassmannians and string theory, Phys. Lett. B 190 55
CrossRef 
 
A. Morozov, 1987 String theory and the structure of universal module space JETP Lett. 45 585

 
A. Morozov, 1987 Pisma Zh. Eksp. Teor. Fiz. 45 457

 
A. Morozov, 1987 Phys. Lett. B 196 325
CrossRef 
 
A.S. Schwarz, 1989 Fermionic string and universal moduli space, Nucl. Phys. B 317 323
CrossRef 
[42]
J. Harer and D. Zagier, 1986 The Euler characteristic of the moduli space of curves I, Invent. Math. 85 457
CrossRef 
 
S.K. Lando and A.K. Zvonkine, 2003 Graphs on surfaces and their applications, Springer, U.S.A.

 
E. Akhmedov and S. Shakirov, Gluing of surfaces with polygonal boundaries, to appear in Funkt. Anal. Pril. [0712.2448]
Preprint 
 
A. Morozov and S. Shakirov, Exact 2-point function in Hermitian matrix model, [0906.0036]
Preprint  SPIRES 
[43]
K. Ueno and K. Takasaki, 1984 Toda lattice hierarchy Adv. Stud. Pure Math. 4 1

[44]
M. Semenov-Tian-Shansky, 1985 Dressing transformations and Poisson group actions Publ. Res. Inst. Math. Sci. Kyoto 21 1237
CrossRef 
 
S. Novikov, S. Manakov, L. Pitaevskii and V.E. Zakharov, 1984 Theory of solitons. The inverse scattering method, Plenum Press, New York U.S.A.

[45]
L. Chekhov and Y. Makeenko, 1992 A hint on the external field problem for matrix models, Phys. Lett. B 278 271 [hep-th/9202006]
CrossRef  Preprint  SPIRES 
 
L. Chekhov and Y. Makeenko, 1992 The multicritical Kontsevich-Penner model, Mod. Phys. Lett. A 7 1223 [hep-th/9201033]
CrossRef  Preprint  SPIRES 
[46]
R. Penner, 1987 Perturbative series and the moduli space of Riemann surfaces J. Diff. Geom. 27 35

[47]
C. Itzykson and J.B. Zuber, 1980 The planar approximation. 2, J. Math. Phys. 21 411
CrossRef 
[48]
L. Chekhov, A. Marshakov, A. Mironov and D. Vasiliev, 2005 Complex geometry of matrix models Proc. Steklov Inst. Math. 251 254 [hep-th/0506075]
Preprint  SPIRES 
[49]
A.S. Alexandrov, A. Mironov and A. Morozov, 2006 Unified description of correlators in non-Gaussian phases of Hermitean matrix model, Int. J. Mod. Phys. A 21 2481 [hep-th/0412099]
CrossRef  Preprint  SPIRES 
 
A.S. Alexandrov, A. Mironov and A. Morozov, 2005 Solving Virasoro constraints in matrix models, Fortsch. Phys. 53 512 [hep-th/0412205]
CrossRef  Preprint  SPIRES 
[50]
R. Dijkgraaf and C. Vafa, 2002 Matrix models, topological strings and supersymmetric gauge theories, Nucl. Phys. B 644 3 [hep-th/0206255]
CrossRef  Preprint  SPIRES 
 
R. Dijkgraaf and C. Vafa, 2002 On geometry and matrix models, Nucl. Phys. B 644 21 [hep-th/0207106]
CrossRef  Preprint  SPIRES 
 
A perturbative window into non-perturbative physics, [hep-th/0208048]
Preprint  SPIRES 
[51]
L. Chekhov and A. Mironov, 2003 Matrix models vs. Seiberg-Witten/Whitham theories, Phys. Lett. B 552 293 [hep-th/0209085]
CrossRef  Preprint  SPIRES 
 
R. Dijkgraaf, S. Gukov, V.A. Kazakov and C. Vafa, 2003 Perturbative analysis of gauged matrix models, Phys. Rev. D 68 045007 [hep-th/0210238]
CrossRef  Preprint  SPIRES 
 
V.A. Kazakov and A. Marshakov, 2003 Complex curve of the two matrix model and its τ-function, J. Phys. A 36 3107 [hep-th/0211236]
IOPscience  Preprint  SPIRES 
 
H. Itoyama and A. Morozov, 2003 The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory, Nucl. Phys. B 657 53 [hep-th/0211245]
CrossRef  Preprint  SPIRES 
 
H. Itoyama and A. Morozov, 2003 Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case, Phys. Lett. B 555 287 [hep-th/0211259]
CrossRef  Preprint  SPIRES 
 
Calculating gluino condensate prepotential, Prog. Theor. Phys. 109 2003 433 [hep-th/0212032]
CrossRef  Preprint  SPIRES 
 
Gluino-condensate (CIV-DV) prepotential from its Whitham-time derivatives, Int. J. Mod. Phys. A 18 2003 5889 [hep-th/0301136]
CrossRef  Preprint  SPIRES 
 
S.G. Naculich, H.J. Schnitzer and N. Wyllard, 2003 Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation J. High Energy Phys. JHEP01(2003)015 [hep-th/0211254]
IOPscience  Preprint  SPIRES 
 
B. Feng, 2003 Geometric dual and matrix theory for SO/Sp gauge theories, Nucl. Phys. B 661 113 [hep-th/0212010]
CrossRef  Preprint  SPIRES 
 
I. Bena, S. de Haro and R. Roiban, 2003 Generalized Yukawa couplings and matrix models, Nucl. Phys. B 664 45 [hep-th/0212083]
CrossRef  Preprint  SPIRES 
 
C.-H. Ahn, 2003 Supersymmetric SO(N)/Sp(N) gauge theory from matrix model: exact mesonic vacua, Phys. Lett. B 560 116 [hep-th/0301011]
CrossRef  Preprint  SPIRES 
 
L. Chekhov, A. Marshakov, A. Mironov and D. Vasiliev, 2003 DV and WDVV, Phys. Lett. B 562 323 [hep-th/0301071]
CrossRef  Preprint  SPIRES 
 
A. Mironov, 2006 Matrix models vs. matrix integrals, Theor. Math. Phys. 146 63 [hep-th/0506158]
CrossRef  Preprint  SPIRES 
 
A. Mironov, 2006 Teor. Mat. Fiz. 146 77
CrossRef 
 
A. Dymarsky and V. Pestun, 2003 On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential, Phys. Rev. D 67 125001 [hep-th/0301135]
CrossRef  Preprint  SPIRES 
 
Y. Ookouchi and Y. Watabiki, 2003 Effective superpotentials for SO/Sp with flavor from matrix models, Mod. Phys. Lett. A 18 1113 [hep-th/0301226]
CrossRef  Preprint  SPIRES 
 
H. Itoyama and H. Kanno, 2003 Supereigenvalue model and Dijkgraaf-Vafa proposal, Phys. Lett. B 573 227 [hep-th/0304184]
CrossRef  Preprint  SPIRES 
 
H. Itoyama and H. Kanno, 2004 Whitham prepotential and superpotential, Nucl. Phys. B 686 155 [hep-th/0312306]
CrossRef  Preprint  SPIRES 
 
M. Matone and L. Mazzucato, 2003 Branched matrix models and the scales of supersymmetric gauge theories J. High Energy Phys. JHEP07(2003)015 [hep-th/0305225]
IOPscience  Preprint  SPIRES 
 
R. Argurio, G. Ferretti and R. Heise, 2004 An introduction to supersymmetric gauge theories and matrix models, Int. J. Mod. Phys. A 19 2015 [hep-th/0311066]
CrossRef  Preprint  SPIRES 
 
M. Gomez-Reino, 2004 Exact superpotentials, theories with flavor and confining vacua J. High Energy Phys. JHEP06(2004)051 [hep-th/0405242]
IOPscience  Preprint  SPIRES 
 
K. Fujiwara, H. Itoyama and M. Sakaguchi, 2005 Supersymmetric U(N) gauge model and partial breaking of N=2 supersymmetry, Prog. Theor. Phys. 113 429 [hep-th/0409060]
CrossRef  Preprint  SPIRES 
 
K. Fujiwara, H. Itoyama and M. Sakaguchi, 2005 Partial breaking of N=2 supersymmetry and of gauge symmetry in the U(N) gauge model, Nucl. Phys. B 723 33 [hep-th/0503113]
CrossRef  Preprint  SPIRES 
 
Supersymmetric U(N) gauge model and partial breaking of N=2 supersymmetry, Prog. Theor. Phys. Suppl. 164 2007 125 [hep-th/0602267]
CrossRef  Preprint  SPIRES 
 
S. Aoyama, 2005 The disc amplitude of the Dijkgraaf-Vafa theory: 1/N expansion vs. complex curve analysis J. High Energy Phys. JHEP10(2005)032 [hep-th/0504162]
IOPscience  Preprint  SPIRES 
 
D. Berenstein and S. Pinansky, Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices, [hep-th/0602294]
Preprint  SPIRES 
[52]
L. Landau and E. Lifshitz, Mechanics, volume 1

[53]
H. Bateman and A. Erdelyi, 1953 Higher transcendental functions, volume 2, London U.K.

[54]
F.A. Berezin and F.I. Karpelevich, 1958 Zonal spherical functions and Laplace operators on some symmetric spaces (in Russian), Dokl. Akad. Nauk SSSR 118 9

 
A.D. Jackson, M.K. Sener and J.J.M. Verbaarschot, 1996 Finite volume partition functions and Itzykson-Zuber integrals, Phys. Lett. B 387 355 [hep-th/9605183]
CrossRef  Preprint  SPIRES 
 
T. Guhr and T. Wettig, 1996 An Itzykson-Zuber-like integral and diffusion for complex ordinary and supermatrices, J. Math. Phys. 37 6395 [hep-th/9605110]
CrossRef  Preprint  SPIRES 
[55]
E. Brézin and V.A. Kazakov, 1990 Exactly solvable field theories of closed strings, Phys. Lett. B 236 144
CrossRef 
 
D.J. Gross and A.A. Migdal, 1990 Nonperturbative two-dimensional quantum gravity, Phys. Rev. Lett. 64 127
CrossRef  PubMed 
 
D.J. Gross and A.A. Migdal, 1990 A nonperturbative treatment of two-dimensional quantum gravity, Nucl. Phys. B 340 333
CrossRef 
 
M. Douglas and S. Shenker, 1990 Strings in less than one dimension, Nucl. Phys. B 335 635
CrossRef 
[56]
S. Kharchev, A. Marshakov, A. Mironov and A. Morozov, 1993 Landau-Ginzburg topological theories in the framework of GKM and equivalent hierarchies Mod. Phys. Lett. A 8 1047 [hep-th/9208046]
CrossRef  Preprint  SPIRES 
 
S. Kharchev, A. Marshakov, A. Mironov and A. Morozov, 1993 Theor. Math. Phys. 95 571
CrossRef 
 
S. Kharchev, A. Marshakov, A. Mironov and A. Morozov, 1993 Teor. Mat. Fiz. 95 280
CrossRef 
[57]
L.K. Hua, 1963 Harmonic analysis of functions of several complex variables in the classical domain, American Mathematical Society, Providence RI U.S.A.

[58]
V.A. Kazakov, 1983 U(&infty;) lattice gauge theory as a free lattice string theory, Phys. Lett. B 128 316
CrossRef 
[59]
L. Chekhov, Matrix models and geometry of moduli spaces, [hep-th/9509001]
Preprint  SPIRES 
 
I.K. Kostov, Conformal field theory techniques in random matrix models, [hep-th/9907060]
Preprint  SPIRES 
[60]
V.S. Dotsenko and V.A. Fateev, 1984 Conformal algebra and multipoint correlation functions in 2 D statistical models, Nucl. Phys. B 240 312
CrossRef 
 
M. Wakimoto, 1986 Fock representations of the affine Lie algebra A1(1), Commun. Math. Phys. 104 605
CrossRef 
 
V. Knizhnik, 1989 Multiloop amplitudes in the theory of quantum strings and complex geometry Usp. Fiz. Nauk 159 401
CrossRef 
 
V. Knizhnik, 1989 Sov. Phys. Usp. 32 945
IOPscience 
 
A. Gerasimov, A. Marshakov, A. Morozov, M. Olshanetsky and S. Shatashvili, 1990 Wess-Zumino-Witten model as a theory of free fields, Int. J. Mod. Phys. A 5 2495
CrossRef 
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