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TMF, 2005, Volume 142, Number 3, Pages 419–488 (Mi tmf1792)  

This article is cited in 23 scientific papers (total in 23 papers)

Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model

A. S. Alexandrovab, A. D. Mironovca, A. Yu. Morozova

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Moscow Institute of Physics and Technology
c P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: Although matrix model partition functions do not exhaust the entire set of $\tau$-functions relevant for string theory, they are elementary blocks for constructing many other $\tau$-functions and seem to capture the fundamental nature of quantum gravity an string theory properly. We propose taking matrix model partition functions as new special functions. This means that they should be investigated and represented in some standard form without reference to particular applications. At the same time, the tables and lists of properties should be sufficiently full to exclude unexpected peculiarities appearing in new applications. Accomplishing this task requires considerable effort, and this paper is only a first step in this direction. We restrict our consideration to the finite Hermitian one-matrix model an concentrate mostly on its phase and branch structure that arises when the partition function is considered as a $D$-module. We discuss the role of the CIV-DV prepotential (which generates a certain basis in the linear space of solutions of the Virasoro constraints, although an understanding of why and how this basis is distinguished is lacking) an evaluate several first multiloop correlators, which generalize the semicircular distribution to the case of multitrace and nonplanar correlators.

Keywords: matrix models, string theory, multiloop correlators

DOI: https://doi.org/10.4213/tmf1792

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English version:
Theoretical and Mathematical Physics, 2005, 142:3, 349–411

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Received: 16.04.2004

Citation: A. S. Alexandrov, A. D. Mironov, A. Yu. Morozov, “Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model”, TMF, 142:3 (2005), 419–488; Theoret. and Math. Phys., 142:3 (2005), 349–411

Citation in format AMSBIB
\by A.~S.~Alexandrov, A.~D.~Mironov, A.~Yu.~Morozov
\paper Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model
\jour TMF
\yr 2005
\vol 142
\issue 3
\pages 419--488
\jour Theoret. and Math. Phys.
\yr 2005
\vol 142
\issue 3
\pages 349--411

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    3. Alexandrov A, Mironov A, Morozov A, “Instantons and merons in matrix models”, Physica D-Nonlinear Phenomena, 235:1–2 (2007), 126–167  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. Dolotin, V, “On the Shapes of Elementary Domains Or Why Mandelbrot Set Is Made From Almost Ideal Circles?”, International Journal of Modern Physics A, 23:22 (2008), 3613  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Morozov A., Shakirov Sh., “On equivalence of two Hurwitz matrix models”, Modern Phys. Lett. A, 24:33 (2009), 2659–2666  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. Alexandrov, A, “Partition Functions of Matrix Models as the First Special Functions of String Theory II. Kontsevich Model”, International Journal of Modern Physics A, 24:27 (2009), 4939  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. 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
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    18. 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
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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