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TMF, 2004, Volume 141, Number 3, Pages 358–374 (Mi tmf129)  

This article is cited in 26 scientific papers (total in 26 papers)

Genus-One Correction to Multicut Matrix Model Solutions

L. O. Chekhov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We calculate genus-one corrections to the Hermitian one-matrix model solution with an arbitrary number of cuts based on the loop equation, confirming the answer previously obtained from algebro-geometric considerations and generalizing it to the case of arbitrary potentials.

Keywords: loop equation, genus expansion, hyperelliptic geometry

DOI: https://doi.org/10.4213/tmf129

Full text: PDF file (264 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2004, 141:3, 1640–1653

Bibliographic databases:

Document Type: Article
Received: 01.04.2004

Citation: L. O. Chekhov, “Genus-One Correction to Multicut Matrix Model Solutions”, TMF, 141:3 (2004), 358–374; Theoret. and Math. Phys., 141:3 (2004), 1640–1653

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. O. Chekhov, A. V. Marshakov, A. D. Mironov, D. Vasiliev, “Complex Geometry of Matrix Models”, Proc. Steklov Inst. Math., 251 (2005), 254–292  mathnet  mathscinet  zmath
    2. Bonelli G, Bonora L, Ricco A, “Conifold geometries, topological strings, and multimatrix models”, Physical Review D, 72:8 (2005), 086001  crossref  mathscinet  adsnasa  isi  scopus  scopus
    3. JETP Letters, 82:3 (2005), 101–104  mathnet  crossref  isi
    4. Eynard B., Orantin N., “Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula”, Journal of High Energy Physics, 2005, no. 12, 034  crossref  mathscinet  isi  scopus  scopus
    5. L. O. Chekhov, “Solving matrix models in $1/N$-expansion”, Russian Math. Surveys, 61:3 (2006), 483–543  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Chekhov L, “Matrix models with hard walls: geometry and solutions”, Journal of Physics A-Mathematical and General, 39:28 (2006), 8857–8893  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Zabrodin A, Wiegmann P, “Large-N expansion for the 2D Dyson gas”, Journal of Physics A-Mathematical and General, 39:28 (2006), 8933–8963  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Chekhov L., Eynard B., “Matrix eigenvalue model: Feynman graph technique for all genera”, Journal of High Energy Physics, 2006, no. 12, 026  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Chekhov L., Eynard B., Orantin N., “Free energy topological expansion for the 2-matrix model”, Journal of High Energy Physics, 2006, no. 12, 053  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Bertoldi G., “Double scaling limits and twisted non-critical superstrings”, Journal of High Energy Physics, 2006, no. 7, 006  crossref  mathscinet  isi  scopus  scopus
    11. Bertoldi G., Hollowood T.J., Miramontes J.L., “Double scaling limits in gauge theories and matrix models”, Journal of High Energy Physics, 2006, no. 6, 045  crossref  mathscinet  isi  scopus  scopus
    12. Chekhov L., Eynard B., “Hermitian matrix model free energy: Feynman graph technique for all genera”, Journal of High Energy Physics, 2006, no. 3, 014  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Eynard B., Orantin N., “Invariants of algebraic curves and topological expansion”, Communications in Number Theory and Physics, 1:2 (2007), 347–452  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Marino M., “Open string amplitudes and large order behavior in topological string theory”, Journal of High Energy Physics, 2008, no. 3, 060  crossref  mathscinet  isi  scopus  scopus
    15. Manabe, M, “Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model”, Nuclear Physics B, 819:1–2 (2009), 35  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    16. Eynard, B, “Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence”, Journal of High Energy Physics, 2009, no. 3, 003  crossref  mathscinet  zmath  isi  scopus  scopus
    17. Flume, R, “A Lagrangean formalism for Hermitean matrix models”, Nuclear Physics B, 812:3 (2009), 322  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    18. Eynard, B, “Topological recursion in enumerative geometry and random matrices”, Journal of Physics A-Mathematical and Theoretical, 42:29 (2009), 293001  crossref  mathscinet  zmath  isi  scopus  scopus
    19. Klitz, A, “Proof of the Lagrangean formalism of Hermitean 1-matrix models to all orders”, Journal of High Energy Physics, 2010, no. 1, 034  crossref  mathscinet  zmath  isi  scopus  scopus
    20. L. O. Chekhov, “Logarithmic potential $\beta$-ensembles and Feynman graphs”, Proc. Steklov Inst. Math., 272 (2011), 58–74  mathnet  crossref  mathscinet  zmath  isi
    21. Andersen J.E. Chekhov L.O. Penner R.C. Reidys Ch.M. Sulkowski P., “Topological Recursion for Chord Diagrams, Rna Complexes, and Cells in Moduli Spaces”, Nucl. Phys. B, 866:3 (2013), 414–443  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    22. Huang M.-x., “Dijkgraaf-Vafa Conjecture and Beta-Deformed Matrix Models”, J. High Energy Phys., 2013, no. 7, 173  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    23. Penner R.C., “Moduli spaces and macromolecules”, Bull. Amer. Math. Soc., 53:2 (2016), 217–268  crossref  mathscinet  zmath  isi  elib  scopus
    24. Eynard B., “Counting Surfaces: Crm Aisenstadt Chair Lectures”, Counting Surfaces: Crm Aisenstadt Chair Lectures, Progress in Mathematical Physics, 70, Birkhauser Boston, 2016, 1–414  crossref  mathscinet  isi
    25. Manabe M. Sulkowski P., “Quantum Curves and Conformal Field Theory”, Phys. Rev. D, 95:12 (2017), 126003  crossref  isi  scopus  scopus
    26. Iwaki K., Marchal O., Saenz A., “Painlevé Equations, Topological Type Property and Reconstruction By the Topological Recursion”, J. Geom. Phys., 124 (2018), 16–54  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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