A. V. Marshakov, “Matrix models, complex geometry, and integrable systems: I”, TMF, 147:2 (2006), 163–228; Theoret. and Math. Phys., 147:2 (2006), 583

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 147, Number 2, Pages 163–228
DOI: https://doi.org/10.4213/tmf1959 (Mi tmf1959)

This article is cited in 11 scientific papers (total in 11 papers)

Matrix models, complex geometry, and integrable systems: I

A. V. Marshakov^ab

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

Full-text PDF (1130 kB) Citations (11)

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DOI: https://doi.org/10.4213/tmf1959

Abstract: We consider the simplest gauge theories given by one- and two-matrix integrals and concentrate on their stringy and geometric properties. We recall the general integrable structure behind the matrix integrals and turn to the geometric properties of planar matrix models, demonstrating that they are universally described in terms of integrable systems directly related to the theory of complex curves. We study the main ingredients of this geometric picture, suggesting that it can be generalized beyond one complex dimension, and formulate them in terms of semiclassical integrable systems solved by constructing tau functions or prepotentials. We discuss the complex curves and tau functions of one- and two-matrix models in detail.

Keywords: string theory, matrix models, complex geometry.

Received: 09.10.2005

English version:
Theoretical and Mathematical Physics, 2006, Volume 147, Issue 2, Pages 583–636
DOI: https://doi.org/10.1007/s11232-006-0065-x

Bibliographic databases:

Language: Russian

Citation: A. V. Marshakov, “Matrix models, complex geometry, and integrable systems: I”, TMF, 147:2 (2006), 163–228; Theoret. and Math. Phys., 147:2 (2006), 583–636

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Linking options:

https://www.mathnet.ru/eng/tmf1959

https://doi.org/10.4213/tmf1959

https://www.mathnet.ru/eng/tmf/v147/i2/p163

Cycle of papers

Matrix models, complex geometry, and integrable systems: I
A. V. Marshakov
TMF, 2006, 147:2, 163–228
Matrix models, complex geometry, and integrable systems: II $^*$
A. V. Marshakov
TMF, 2006, 147:3, 399–449

This publication is cited in the following 11 articles:

G. F. Helminck, J. A. Weenink, “LU Factorizations for ℕ × ℕ-Matrices and Solutions of the k[S]-Hierarchy and Its Strict Version”, Geometry, 2:2 (2025), 4
Araujo T., “Comments on Slavnov Products, Temperley-Lieb Open Spin Chains, and Kp Tau Functions”, Nucl. Phys. B, 972 (2021), 115566
Björn Gustafsson, Yu-Lin Lin, Lecture Notes in Mathematics, 2287, Laplacian Growth on Branched Riemann Surfaces, 2021, 99
Björn Gustafsson, Trends in Mathematics, Analysis as a Life, 2019, 213
O. S. Kruglinskaya, “Correlation functions and spectral curves in models of minimal gravity”, Theoret. and Math. Phys., 174:1 (2013), 78–85
A. V. Marshakov, “Gauge theories as matrix models”, Theoret. and Math. Phys., 169:3 (2011), 1704–1723
Marshakov A., Mironov A., Morozov A., “On AGT relations with surface operator insertion and a stationary limit of beta-ensembles”, J Geom Phys, 61:7 (2011), 1203–1222
A. V. Marshakov, “On the microscopic origin of integrability in the Seiberg–Witten theory”, Theoret. and Math. Phys., 154:3 (2008), 362–384
Vazquez SE, “Reconstructing 1/2 BPS space-time metrics from matrix models and spin chains”, Physical Review D, 75:12 (2007), 125012
A. V. Marshakov, “Matrix models, complex geometry, and integrable systems: II$^*$”, Theoret. and Math. Phys., 147:3 (2006), 777–820
Fukuma M., Irie H., Matsuo Y., “Notes on the algebraic curves in (p, q) minimal string theory”, Journal of High Energy Physics, 2006, no. 9, 075

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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