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 The Chiral Supereigenvalue Model

1997 ◽  
Vol 12 (24) ◽  
pp. 1745-1758 ◽  
Author(s):  
Gernot Akemann ◽  
Jan C. Plefka
Keyword(s):  
Free Energy ◽  
Matrix Model ◽  
Correlation Functions ◽  
Iterative Scheme ◽  
Higher Genus ◽  
Genus One

A supereigenvalue model with purely positive bosonic eigenvalues is presented and solved by considering its superloop equations. This model represents the supersymmetric generalization of the complex one-matrix model, in analogy to the relation between the supereigenvalue and the Hermitian one-matrix model. Closed expressions for all planar multi-superloop correlation functions are found. Moreover an iterative scheme allows the calculation of higher genus contributions to the free energy and the correlators. Explicit results for genus one are given.

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.

DECONFINEMENT TEMPERATURES FOR SMOOTH STRINGS

1989 ◽  
Vol 04 (01) ◽  
pp. 99-106 ◽  
Author(s):  
XIAOAN ZHOU ◽  
K. S. VISWANATHAN
Keyword(s):  
Free Energy ◽  
Riemann Surfaces ◽  
Reasonable Agreement ◽  
Gauge Theories ◽  
Path Integrals ◽  
String Tension ◽  
Monte Carlo Data ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Genus One

Deconfinement temperatures for smooth strings are obtained by analyzing the free energy of a collection of smooth string excitations. This corresponds to evaluating path integrals on genus one Riemann surfaces. We find that [Formula: see text], where σ is the string tension, for closed smooth strings and [Formula: see text] for open smooth strings, in reasonable agreement with Monte Carlo data for SU(3) lattice gauge theories.

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 Quantum periods and spectra in dimer models and Calabi-Yau geometries

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Min-xin Huang ◽  
Yuji Sugimoto ◽  
Xin Wang
Keyword(s):  
Free Energy ◽  
Perturbation Method ◽  
Integrable Systems ◽  
Differential Operators ◽  
Topological String ◽  
Quantum Systems ◽  
Quantum Integrable Systems ◽  
Topological Vertex ◽  
Higher Genus ◽  
Genus One

Abstract We study a class of quantum integrable systems derived from dimer graphs and also described by local toric Calabi-Yau geometries with higher genus mirror curves, generalizing some previous works on genus one mirror curves. We compute the spectra of the quantum systems both by standard perturbation method and by Bohr-Sommerfeld method with quantum periods as the phase volumes. In this way, we obtain some exact analytic results for the classical and quantum periods of the Calabi-Yau geometries. We also determine the differential operators of the quantum periods and compute the topological string free energy in Nekrasov-Shatashvili (NS) limit. The results agree with calculations from other methods such as the topological vertex.

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
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