Free energy of the two matrix model / dToda tau function - INSPIRE

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Free energy of the two matrix model / dToda tau function

M. Bertola
(
- Concordia U., Math. Dept. and
- Montreal U., CRM
)

Jun, 2003

19 pages

Published in:

Nucl.Phys.B 669 (2003) 435-461

e-Print:

hep-th/0306184 [hep-th]

DOI:

10.1016/j.nuclphysb.2003.07.029

Report number:

CRM-2921-2003

View in:

reference search27 citations

Citations per year

Abstract:

We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the tau-function of the dispersionless two--dimensional Toda hierarchy. The formula generalizes the case studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan in the case of conformal maps of Jordan curves. Finally we generalize the formula found in genus zero to the case of spectral curves of arbitrary genus with certain fixed data.

02.30.Jr
05.90.+m
matrix model
energy
differential equations: Toda
hierarchy
tau-function

References(25)

Figures(0)

String orthogonal polynomials, string equations, and 2 Toda symmetries

M. Adler
(
- Brandeis U.
)
,
P. van Moerbeke
(
- Louvain U.
)

- Commun.Pure Appl.Math. 50 (1997) 241-290
•
e-Print:
- hep-th/9706182

The Spectrum of coupled random matrices

Mark Adler
(
- Brandeis U.
)
,
Pierre van Moerbeke
(
- Louvain U. and
- Brandeis U.
)

- Annals Math. 149 (1999) 921-976
•
e-Print:
- hep-th/9907213
•
DOI:
- 10.2307/121077

M theory as a matrix model: A conjecture

Tom Banks
(
- Rutgers U., Piscataway
)
,
W. Fischler
(
- Texas U.
)
,
S.H. Shenker
(
- Rutgers U., Piscataway
)
,
Leonard Susskind
(
- Stanford U., Phys. Dept.
)

- ,
- Phys.Rev.D 55 (1997) 5112-5128,
•
e-Print:
- hep-th/9610043
•
DOI:
- 10.1201/9781482268737-37

e-Print:
- math/0205160

Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem

M. Bertola
(
- Montreal U., CRM and
- Concordia U., Math. Dept.
)
,
B. Eynard
(
- Montreal U., CRM and
- Saclay, SPhT
)
,
J. Harnad
(
- Montreal U., CRM and
- Concordia U., Math. Dept.
)

- Commun.Math.Phys. 243 (2003) 193-240
•
e-Print:
- nlin/0208002
•
DOI:
- 10.1007/s00220-003-0934-1

- Theor.Math.Phys. 134 25

Duality, biorthogonal polynomials and multimatrix models

M. Bertola
(
- Montreal U., CRM and
- Concordia U., Math. Dept.
)
,
B. Eynard
(
- Montreal U., CRM and
- Saclay
)
,
John P. Harnad
(
- Montreal U., CRM and
- Concordia U., Math. Dept.
)

- Commun.Math.Phys. 229 (2002) 73-120
•
e-Print:
- nlin/0108049
•
DOI:
- 10.1007/s002200200663

Mixed correlation functions of the two matrix model

M. Bertola
(
- Concordia U., Math. Dept. and
- Montreal U., CRM
)
,
B. Eynard
(
- Montreal U., CRM and
- Saclay
)

- J.Phys.A 36 (2003) 7733-7750
•
e-Print:
- hep-th/0303161
•
DOI:
- 10.1088/0305-4470/36/28/304

Integrability in SFT and new representation of KP tau function

Alexey Boyarsky
(
- Bohr Inst.
)
,
Oleg Ruchayskiy
(
- Chicago U., EFI and
- Chicago U.
)

- JHEP 03 (2003) 027
•
e-Print:
- hep-th/0211010
•
DOI:
- 10.1088/1126-6708/2003/03/027

Planar Diagrams, Two-Dimensional Lattice Gravity and Surface Models

F. David
(
- Saclay
)

- Nucl.Phys.B 257 (1985) 45,
•
DOI:
- 10.1016/0550-3213(85)90335-9

2-D Gravity and random matrices

- Phys.Rept. 254 (1995) 1-133
•
e-Print:
- hep-th/9306153
•
DOI:
- 10.1016/0370-1573(94)00084-G

Random matrix theories in quantum physics: Common concepts

- Phys.Rept. 299 (1998) 189-425
•
e-Print:
- cond-mat/9707301
•
DOI:
- 10.1016/S0370-1573(97)00088-4

Ising model on a dynamical planar random lattice: Exact solution

V.A. Kazakov
(
- Moscow, Space Res. Inst.
)

- Phys.Lett.A 119 (1986) 140-144
•
DOI:
- 10.1016/0375-9601(86)90433-0

Complex curve of the two matrix model and its tau function

Vladimir A. Kazakov
(
- Ecole Normale Superieure
)
,
Andrei Marshakov
(
- Ecole Normale Superieure and
- IHES, Bures-sur-Yvette and
- Lebedev Inst. and
- Moscow, ITEP
)

- J.Phys.A 36 (2003) 3107-3136
•
e-Print:
- hep-th/0211236
•
DOI:
- 10.1088/0305-4470/36/12/315

Integrable structure of the Dirichlet boundary problem in two-dimensions

A. Marshakov
(
- Lebedev Inst.
)
,
P. Wiegmann
(
- Chicago U. and
- Chicago U., EFI and
- Landau Inst.
)
,
A. Zabrodin
(
- RAS, Inst. Biochem. Phys. and
- Moscow, ITEP
)

- Commun.Math.Phys. 227 (2002) 131-153
•
e-Print:
- hep-th/0109048
•
DOI:
- 10.1007/s002200200629

- Phys.Rev.Lett. 84 4882

Quasiclassical limit of Toda hierarchy and W(infinity) symmetries

- Lett.Math.Phys. 28 (1993) 165-176
•
e-Print:
- hep-th/9301070
•
DOI:
- 10.1007/BF00745148

Free bosons and tau functions for compact Riemann surfaces and closed smooth Jordan curves. 1. Current correlation functions

Leon A. Takhtajan
(
- Yale U., Math. Dept. and
- Yale U.
)

- Lett.Math.Phys. 56 (2001) 181-228
•
e-Print:
- math/0102164
•
DOI:
- 10.1023/A:1017999407650

Analytic functions and integrable hierarchies characterization of tau functions

Lee Peng Teo
(
- Taiwan, Natl. Chiao Tung U.
)

e-Print:
- hep-th/0305005

Toda lattice hierarchy

- Adv.Stud.Pure Math. 4 (1984) 1-05

Random matrix model approach to chiral symmetry

J.J.M. Verbaarschot
(
- SUNY, Stony Brook
)

- Nucl.Phys.B Proc.Suppl. 53 (1997) 88-94,
- Lattice 96:88-94
•
e-Print:
- hep-lat/9607086
•
DOI:
- 10.1016/S0920-5632(96)00602-0

Conformal maps and dispersionless integrable hierarchies

P.B. Wiegmann
(
- Chicago U., EFI and
- Landau inst.
)
,
A. Zabrodin
(
- Moscow, Inst. Chem. Phys. and
- Moscow, ITEP
)

- Commun.Math.Phys. 213 (2000) 523-538
•
e-Print:
- hep-th/9909147
•
DOI:
- 10.1007/s002200000249

Dispersionless limit of Hirota equations in some problems of complex analysis

A. Zabrodin
(
- RAS, Inst. Biochem. Phys. and
- Moscow, ITEP
)

- Theor.Math.Phys. 129 (2001) 1511-1525,
- Teor.Mat.Fiz. 129 (2001) 239-257
•
e-Print:
- math/0104169
•
DOI:
- 10.1023/A:1012883123413