메뉴 건너뛰기




Volumn 2009, Issue 3, 2009, Pages

Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence

Author keywords

Differential and algebraic geometry; Matrix models; Topological strings

Indexed keywords


EID: 67649553450     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2009/03/003     Document Type: Article
Times cited : (58)

References (38)
  • 1
    • 37449025111 scopus 로고    scopus 로고
    • Topological strings and (almost) modular forms
    • M. Aganagic, V. Bouchard and A. Klemm, 2008 Topological strings and (almost) modular forms, Commun. Math. Phys. 277 771 [hep-th/0607100]
    • (2008) Commun. Math. Phys. , vol.277 , pp. 771
    • Aganagic, M.1    Bouchard, V.2    Klemm, A.3
  • 3
    • 0346995411 scopus 로고    scopus 로고
    • Differential systems for bi-orthogonal polynomials appearing in two-matrix models and the associated Riemann-Hilbert problem
    • M. Bertola, B. Eynard, J. Harnad, 2003 Differential systems for bi-orthogonal polynomials appearing in two-matrix models and the associated Riemann-Hilbert problem, Comm. Math. Phys. 243 193 [nlin/0208002]
    • (2003) Comm. Math. Phys. , vol.243 , pp. 193
    • Bertola, M.1    Eynard, B.2    Harnad, J.3
  • 4
    • 0037471328 scopus 로고    scopus 로고
    • Partition functions for matrix models and isomonodromic τ functions
    • M. Bertola, B. Eynard and J. Harnad, 2003 Partition functions for matrix models and isomonodromic τ functions, J. Phys. A 36 3067 [nlin/0204054]
    • (2003) J. Phys. , vol.36 , Issue.12 , pp. 3067
    • Bertola, M.1    Eynard, B.2    Harnad, J.3
  • 8
    • 13444256444 scopus 로고
    • Holomorphic anomalies in topological field theories
    • M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, 1993 Holomorphic anomalies in topological field theories, Nucl. Phys. B 405 279 [hep-th/9302103]
    • (1993) Nucl. Phys. , vol.405 , pp. 279
    • Bershadsky, M.1    Cecotti, S.2    Ooguri, H.3    Vafa, C.4
  • 9
    • 0034730267 scopus 로고    scopus 로고
    • Breakdown of universality in multi-cut matrix models
    • G. Bonnet, F. David and B. Eynard, 2000 Breakdown of universality in multi-cut matrix models, J. Phys. A33 6739 [condmat/0003324]
    • (2000) J. Phys. , vol.33 , pp. 6739
    • Bonnet, G.1    David, F.2    Eynard, B.3
  • 12
    • 10344257271 scopus 로고    scopus 로고
    • Genus one correlation to multi-cut matrix model solutions
    • L. Chekhov, 2004 Genus one correlation to multi-cut matrix model solutions, Theor. Math. Phys. 141 1640 [hep-th/0401089]
    • (2004) Theor. Math. Phys. , vol.141 , pp. 1640
    • Chekhov, L.1
  • 13
    • 33846158147 scopus 로고    scopus 로고
    • Free energy topological expansion for the 2-matrix model
    • L. Chekhov, B. Eynard and N. Orantin, 2006 Free energy topological expansion for the 2-matrix model, J. High Energy Phys. JHEP12(2006)053 [math-ph/0603003]
    • (2006) J. High Energy Phys. , vol.2006 , Issue.12 , pp. 053
    • Chekhov, L.1    Eynard, B.2    Orantin, N.3
  • 14
    • 0033440723 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
    • P.A. Deift, T. Kriecherbauer, K. T-R. McLaughlin, S. Venakides and Z. Zhou, 1999 Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Commun. Pure Appl. Math. 52 1335
    • (1999) Commun. Pure Appl. Math. , vol.52 , pp. 1335
    • Deift, P.A.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, Z.5
  • 16
    • 0038239560 scopus 로고    scopus 로고
    • Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques and applications to graphical enumeration
    • N.M. Ercolani and K.D.T-R McLaughlin, 2003 Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques and applications to graphical enumeration, Int. Math. Res. Not. 14 755 [math-ph/0211022]
    • (2003) Int. Math. Res. Not. , vol.2003 , Issue.14 , pp. 755
    • Ercolani, N.M.1    McLaughlin K.D.T-R2
  • 17
    • 23044467437 scopus 로고    scopus 로고
    • Topological expansion for the 1-hermitian matrix model correlation functions
    • B. Eynard, 2004 Topological expansion for the 1-hermitian matrix model correlation functions, J. High Energy Phys. JHEP11(2004)031 [hep-th/0407261]
    • (2004) J. High Energy Phys. , vol.2004 , Issue.11 , pp. 031
    • Eynard, B.1
  • 19
    • 34547655742 scopus 로고    scopus 로고
    • Holomorphic anomaly and matrix models
    • B. Eynard, M. Marĩo and N. Orantin, 2007 Holomorphic anomaly and matrix models, J. High Energy Phys. JHEP06(2007)058 [hep-th/0702110]
    • (2007) J. High Energy Phys. , vol.2007 , Issue.6 , pp. 058
    • Eynard, B.1    Marĩo, M.2    Orantin, N.3
  • 20
    • 33846138678 scopus 로고    scopus 로고
    • Hermitean matrix model free energy: Feynman graph technique for all genera
    • 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]
    • (2006) J. High Energy Phys. , vol.2006 , Issue.3 , pp. 014
    • Chekhov, L.1    Eynard, B.2
  • 21
    • 33645528923 scopus 로고    scopus 로고
    • Topological expansion of the 2-matrix model correlation functions: Diagrammatic rules for a residue formula
    • 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]
    • (2005) J. High Energy Phys. , vol.2005 , Issue.12 , pp. 034
    • Eynard, B.1    Orantin, N.2
  • 24
    • 0031521153 scopus 로고    scopus 로고
    • Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices
    • B. Eynard, 1997 Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices, Nucl. Phys. B 506 633 [condmat/9707005]
    • (1997) Nucl. Phys. , vol.506 , pp. 633
    • Eynard, B.1
  • 29
    • 0001283085 scopus 로고
    • The isomonodromy approach to matrix models in 2D quantum gravity
    • A. Fokas, A. Its and A. Kitaev, 1992 The isomonodromy approach to matrix models in 2D quantum gravity, Commun. Math. Phys. 147 395
    • (1992) Commun. Math. Phys. , vol.147 , pp. 395
    • Fokas, A.1    Its, A.2    Kitaev, A.3
  • 30
    • 51949086516 scopus 로고    scopus 로고
    • Second order asymptotics for matrix models
    • A. Guionnet and E. Segara Maurel, 2007 Second order asymptotics for matrix models, Prob. Ann. 35 2160 [Math.PR/0601040]
    • (2007) Prob. Ann. , vol.35 , Issue.6 , pp. 2160
    • Guionnet, A.1    Segara Maurel, E.2
  • 31
    • 17144426793 scopus 로고
    • Ising model on a dynamical planar random lattice: Exact solution
    • V.A. Kazakov, 1986 Ising model on a dynamical planar random lattice: exact solution, Phys. Lett. A 119 140
    • (1986) Phys. Lett. , vol.119 , pp. 140
    • Kazakov, V.A.1
  • 32
    • 49149137872 scopus 로고
    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients i
    • M. Jimbo, T. Miwa and K. Ueno, 1981 Monodromy preserving deformation of linear ordinary differential equations with rational coefficients I, Physica D 2 306
    • (1981) Physica , vol.2 , pp. 306
    • Jimbo, M.1    Miwa, T.2    Ueno, K.3
  • 33
    • 0001792752 scopus 로고
    • Intersection theory on the moduli space of curves and the matrix Airy function
    • M. Kontsevitch, 1992 Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 1 [MPI/91-47] [MPI/91-77]
    • (1992) Comm. Math. Phys. , vol.147 , pp. 1
    • Kontsevitch, M.1
  • 37
    • 0000693589 scopus 로고
    • A census of planar maps
    • W.T. Tutte, 1963 A census of planar maps, Can. J. Math. 15 249
    • (1963) Can. J. Math. , vol.15 , pp. 249
    • Tutte, W.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.