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

2003 ◽  
Vol 669 (3) ◽  
pp. 435-461 ◽  
Author(s):  
M. Bertola
Keyword(s):  
Free Energy ◽  
Matrix Model ◽  
Tau Function

scholarly journals Complex curve of the two-matrix model and its tau-function

2003 ◽  
Vol 36 (12) ◽  
pp. 3107-3136 ◽  
Author(s):  
Vladimir A Kazakov ◽  
Andrei Marshakov
Keyword(s):  
Matrix Model ◽  
Tau Function ◽  
Complex Curve

A CRITICAL MATRIX MODEL AT c=1

1991 ◽  
Vol 06 (03) ◽  
pp. 259-270 ◽  
Author(s):  
JACQUES DISTLER ◽  
CUMRUN VAFA
Keyword(s):  
Free Energy ◽  
Euler Characteristic ◽  
Matrix Model ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Continuum Theory ◽  
Critical Limit ◽  
Logarithmic Corrections

By taking the critical limit of Penner’s matrix model we obtain a continuum theory whose free energy at genus-g is the Euler characteristic of moduli space of Riemann surfaces of genus-g. The exponents, and the appearance of logarithmic corrections suggest that we are dealing with a theory at c=1.

scholarly journals Determinant formulas for matrix model free energy

JETP Letters ◽  
2005 ◽  
Vol 82 (3) ◽  
pp. 101-104 ◽  
Author(s):  
D. Vasiliev
Keyword(s):  
Free Energy ◽  
Matrix Model ◽  
Model Free

scholarly journals 1/N2 Correction to Free Energy in Hermitian Two-Matrix Model

2005 ◽  
Vol 71 (3) ◽  
pp. 199-207 ◽  
Author(s):  
B. Eynard ◽  
A. Kokotov ◽  
D. Korotkin
Keyword(s):  
Free Energy ◽  
Matrix Model

ON THE BEHAVIOR OF STATISTICAL SUM OF A MODEL WITH YANG–LEE SINGULARITY NEAR CRITICAL POINT

1992 ◽  
Vol 07 (01) ◽  
pp. 21-23 ◽  
Author(s):  
D. B. SAHAKYAN
Keyword(s):  
Free Energy ◽  
Critical Point ◽  
Matrix Model

An one-matrix model of singularities on the torus has been investigated. We calculate the value of discontinuity of free energy asymptotics which tends to an infinity number of lattice sites at the critical point.

scholarly journals Genus one contribution to free energy in Hermitian two-matrix model

2004 ◽  
Vol 694 (3) ◽  
pp. 443-472 ◽  
Author(s):  
B Eynard ◽  
A Kokotov ◽  
D Korotkin
Keyword(s):  
Free Energy ◽  
Matrix Model ◽  
Genus One

scholarly journals ϵ-CORRECTED SEIBERG–WITTEN PREPOTENTIAL OBTAINED FROM HALF-GENUS EXPANSION IN β-DEFORMED MATRIX MODEL

2011 ◽  
Vol 26 (20) ◽  
pp. 3439-3467 ◽  
Author(s):  
H. ITOYAMA ◽  
N. YONEZAWA
Keyword(s):  
Free Energy ◽  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Partition Function ◽  
Matrix Model ◽  
Conformal Block ◽  
Supersymmetric Gauge ◽  
Genus Expansion ◽  
Resolvent Function ◽  
Explicit Expressions

We consider the half-genus expansion of the resolvent function in the β-deformed matrix model with three-Penner potential under the AGT conjecture and the 0d–4d dictionary. The partition function of the model, after the specification of the paths, becomes the DF conformal block for fixed c and provides the Nekrasov partition function expanded both in [Formula: see text] and in ϵ = ϵ1+ϵ2. Exploiting the explicit expressions for the lower terms of the free energy extracted from the above expansion, we derive the first few ϵ corrections to the Seiberg–Witten prepotential in terms of the parameters of SU(2), Nf = 4, [Formula: see text] supersymmetric gauge theory.

scholarly journals Free energy topological expansion for the 2-matrix model

2006 ◽  
Vol 2006 (12) ◽  
pp. 053-053 ◽  
Author(s):  
Leonid Chekhov ◽  
Bertrand Eynard ◽  
Nicolas Orantin
Keyword(s):  
Free Energy ◽  
Matrix Model ◽  
Topological Expansion

THE STRING DIFFERENCE EQUATION OF THE D=1 MATRIX MODEL AND W1+∞ SYMMETRY OF THE KP HIERARCHY

1992 ◽  
Vol 07 (20) ◽  
pp. 4791-4802 ◽  
Author(s):  
M.A. AWADA ◽  
S.J. SIN
Keyword(s):  
Free Energy ◽  
String Theory ◽  
Difference Equation ◽  
Matrix Model ◽  
Zero Mode ◽  
Legendre Transformation ◽  
Kp Hierarchy ◽  
Kdv Hierarchy ◽  
The Difference ◽  
Special Case

We give a connection between the D=1 matrix model and the generalized KP hierarchy. First, we find a difference equation satisfied by F, the Legendre transformation of the free energy of the D=1 matrix model on a circle of radius R. Then we show that it is a special case of the difference equation of the generalized KP hierarchy with its zero mode identified with the scaling variable of the D=1 string theory. We propose that the massive D=1 matrix model is described by the generalized KP hierarchy, which implies the manifest integrability of D=1 string theory. We also show that the (generalized) KP hierarchy has an underlying W1+∞ symmetry. By reduction, we prove that the generalized KdV hierarchy has a subalgebra of the above symmetry which again forms a W1+∞. We argue that there are no W constraints in D=1 string theory, which is in contrast to D<1 theories, where there are W1+∞ constraints.

THE PENNER MATRIX MODEL AND c = 1 STRINGS

1991 ◽  
Vol 06 (18) ◽  
pp. 1665-1677 ◽  
Author(s):  
S. CHAUDHURI ◽  
H. DYKSTRA ◽  
J. LYKKEN
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Matrix Model ◽  
Critical Radius ◽  
Scaling Limit ◽  
Legendre Transform ◽  
Complex Eigenvalue ◽  
Closed Contour ◽  
Branch Points ◽  
Double Scaling Limit

The steepest descent solution of the Penner matrix model has a one-cut eigenvalue support. Criticality results when the two branch points of this support coalesce. The support is then a closed contour in the complex eigenvalue plane. Simple generalizations of the Penner model have multi-cut solutions. For these models, the eigenvalue support at criticality is also a closed contour, but consisting of several cuts. We solve the simplest such model, which we call the KT model, in the double-scaling limit. Its free energy is a Legendre transform of the free energy of the c = 1 string compactified to the critical radius of the Kosterlitz–Thouless phase transition.

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