scholarly journals Double scaling limit in the random matrix model: The Riemann-Hilbert approach

2003 ◽  
Vol 56 (4) ◽  
pp. 433-516 ◽  
Author(s):  
Pavel M. Bleher ◽  
Alexander R. Its
Keyword(s):  
Matrix Model ◽  
Random Matrix ◽  
Scaling Limit ◽  
Random Matrix Model ◽  
Double Scaling Limit

scholarly journals Painlevé I double scaling limit in the cubic random matrix model

2016 ◽  
Vol 05 (02) ◽  
pp. 1650004 ◽  
Author(s):  
Pavel Bleher ◽  
Alfredo Deaño
Keyword(s):  
Asymptotic Behavior ◽  
Partition Function ◽  
Matrix Model ◽  
Random Matrix ◽  
Scaling Limit ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Recurrence Coefficients ◽  
Random Matrix Model ◽  
Double Scaling Limit

We obtain the double scaling asymptotic behavior of the recurrence coefficients and the partition function at the critical point of the [Formula: see text] Hermitian random matrix model with cubic potential. We prove that the recurrence coefficients admit an asymptotic expansion in powers of [Formula: see text], and in the leading order the asymptotic behavior of the recurrence coefficients is given by a Boutroux tronquée solution to the Painlevé I equation. We also obtain the double scaling limit of the partition function, and we prove that the poles of the tronquée solution are limits of zeros of the partition function. The tools used include the Riemann–Hilbert approach and the Deift–Zhou nonlinear steepest descent method for the corresponding family of complex orthogonal polynomials and their recurrence coefficients, together with the Toda equation in the parameter space.

scholarly journals Extremal correlators and random matrix theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Alba Grassi ◽  
Zohar Komargodski ◽  
Luigi Tizzano
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Matrix Model ◽  
Effective Field Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Effective Field ◽  
Random Matrix Model ◽  
Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

scholarly journals Asymptotics of the partition function of a random matrix model

2005 ◽  
Vol 55 (6) ◽  
pp. 1943-2000 ◽  
Author(s):  
Pavel M. Bleher ◽  
Alexander Its
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Random Matrix ◽  
Random Matrix Model

Random-matrix model for hot metallic clusters

1995 ◽  
Vol 51 (5) ◽  
pp. 3902-3910 ◽  
Author(s):  
C. Brechignac ◽  
Ph. Cahuzac ◽  
J. Leyginer ◽  
A. Sarfati ◽  
V. M. Akulin
Keyword(s):  
Matrix Model ◽  
Random Matrix ◽  
Metallic Clusters ◽  
Random Matrix Model

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

Sign in / Sign up

Export Citation Format

Share Document