Instantons and merons in matrix models

Alexandrov, A.S.; Mironov, A.; Morozov, A.

doi:10.1016/j.physd.2007.04.018

Instantons and merons in matrix models

A.S. Alexandrov
(
- Moscow, ITEP
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)

Aug, 2006

54 pages

Published in:

Physica D 235 (2007) 126-167

e-Print:

hep-th/0608228 [hep-th]

DOI:

10.1016/j.physd.2007.04.018

Report number:

FIAN-TD-2-06,
ITEP-TH-107-05

View in:

pdf

reference search119 citations

Citations per year

Abstract:

Various branches of matrix model partition function can be represented as intertwined products of universal elementary constituents: Gaussian partition functions Z_G and Kontsevich tau-functions Z_K. In physical terms, this decomposition is the matrix-model version of multi-instanton and multi-meron configurations in Yang-Mills theories. Technically, decomposition formulas are related to representation theory of algebras of Krichever-Novikov type on families of spectral curves with additional Seiberg-Witten structure. Representations of these algebras are encoded in terms of the global partition functions. They interpolate between Z_G and Z_K associated with different singularities on spectral Riemann surfaces. This construction is nothing but M-theory-like unification of various matrix models with explicit and representative realization of dualities.

Loop equations
Matrix models
M-theory
matrix model
partition function
meron
instanton
algebra: Virasoro
algebra: Krichever-Novikov
algebra: representation

References(103)

Figures(0)

[1]

Partition functions of matrix models as the first special functions of string theory. 1. Finite size Hermitean one matrix model

- Int.J.Mod.Phys.A 19 (2004) 4127-4165
•
e-Print:
- hep-th/0310113
•
DOI:
- 10.1142/S0217751X04018245

[1]

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

- Theor.Math.Phys. 142 (2005) 349-411,
- Teor.Mat.Fiz. 142 (2005) 419-488
•
DOI:
- 10.1007/s11232-005-0031-z

[1]

Partition functions of matrix models as the first special functions of string theory. 1. Finite size Hermitean one matrix model

- Int.J.Mod.Phys.A 19 (2004) 4127-4165
•
e-Print:
- hep-th/0310113
•
DOI:
- 10.1142/S0217751X04018245

[2]

Challenges of matrix models

A. Morozov
(
- Moscow, ITEP
)

[2]

Matrix models vs. matrix integrals

A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)

- Theor.Math.Phys. 146 (2006) 63-72,
- Teor.Mat.Fiz. 146 (2006) 77-89
•
e-Print:
- hep-th/0506158
•
DOI:
- 10.1007/s11232-006-0007-7

[3]

Random Matrices, 2nd ed

M.L. Mehta

[3]

Planar Diagrams

- Commun.Math.Phys. 59 (1978) 35
•
DOI:
- 10.1007/BF01614153

[3]

A New Method in the Combinatorics of the Topological Expansion

D. Bessis
(
- Saclay
)

- Commun.Math.Phys. 69 (1979) 147
•
DOI:
- 10.1007/BF01221445

[3]

Quantum field theory techniques in graphical enumeration

- Adv.Appl.Math. 1 (1980) 109-157
•
DOI:
- 10.1016/0196-8858(80)90008-1

[3]

The Planar Approximation. 2.

C. Itzykson
(
- Saclay
)
,
J.B. Zuber
(
- Saclay
)

- J.Math.Phys. 21 (1980) 411,
- In *Bad Honnef 1980, Proceedings, Current Problems In Particle Theory*, 137-159
•
DOI:
- 10.1063/1.524438

[4]

Matrix models of 2-D gravity and Toda theory

- Nucl.Phys.B 357 (1991) 565-618
•
DOI:
- 10.1016/0550-3213(91)90482-D

[5]

Integrability and matrix models

A. Morozov
(
- Moscow, ITEP
)

- Phys.Usp. 37 (1994) 1-55,
- Phys. Usp. 37 (1994) 1-55 No. 1 (Usp. Fiz. Nauk 164 (1994) 3-62 No. 1), and Moscow Inst. Theor. Exp. Phys. - ITEF-93-002 (93/03,rec.Apr.) 152 p. (306959
•
e-Print:
- hep-th/9303139
•
DOI:
- 10.1070/PU1994v037n01ABEH000001