scholarly journals On the Structure of Correlation Functions in the Normal Matrix Model

1998 ◽  
Vol 196 (1) ◽  
pp. 203-247 ◽  
Author(s):  
Ling-Lie Chau ◽  
Oleg Zaboronsky
Keyword(s):  
Matrix Model ◽  
Correlation Functions ◽  
Normal Matrix

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 W-INFINITY WARD IDENTITIES AND CORRELATION FUNCTIONS IN THE c=1 MATRIX MODEL

1992 ◽  
Vol 07 (11) ◽  
pp. 937-953 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
GAUTAM MANDAL ◽  
SPENTA R. WADIA
Keyword(s):  
Matrix Model ◽  
Correlation Functions ◽  
Scaling Limit ◽  
Three Dimensional ◽  
Dimensional Theory ◽  
Fermionic Field ◽  
Ward Identities ◽  
The Matrix ◽  
Dependent Potential ◽  
General Time

We explore consequences of W-infinity symmetry in the fermionic field theory of the c=1 matrix model. We derive exact Ward identities relating correlation functions of the bilocal operator. These identities can be expressed as equations satisfied by the effective action of a three-dimensional theory and contain non-perturbative information about the model. We use these identities to calculate the two-point function of the bilocal operator in the double scaling limit. We extract the operator whose two-point correlator has a single pole at an (imaginary) integer value of the energy. We then rewrite the W-infinity charges in terms of operators in the matrix model and use this to derive constraints satisfied by the partition function of the matrix model with a general time dependent potential.

scholarly journals Mixed correlation functions of the two-matrix model

2003 ◽  
Vol 36 (28) ◽  
pp. 7733-7750 ◽  
Author(s):  
M Bertola ◽  
B Eynard
Keyword(s):  
Matrix Model ◽  
Correlation Functions

Correlation functions and phase structure of the three-matrix model

1991 ◽  
Vol 254 (1-2) ◽  
pp. 81-88 ◽  
Author(s):  
Maximilian Kreuzer
Keyword(s):  
Matrix Model ◽  
Correlation Functions ◽  
Phase Structure

Critical potentials and correlation functions in the minus two dimensional matrix model

1991 ◽  
Vol 354 (2-3) ◽  
pp. 475-495 ◽  
Author(s):  
Igor R. Klebanov ◽  
Richard B. Wilkinson
Keyword(s):  
Matrix Model ◽  
Correlation Functions ◽  
Two Dimensional ◽  
Dimensional Matrix

scholarly journals THREE-POINT FUNCTIONS OF NON-UNITARY MINIMAL MATTER COUPLED TO GRAVITY

1993 ◽  
Vol 08 (03) ◽  
pp. 197-207 ◽  
Author(s):  
DEBASHIS GHOSHAL ◽  
SWAPNA MAHAPATRA
Keyword(s):  
Matrix Model ◽  
Correlation Functions ◽  
The Other ◽  
Tree Level ◽  
Minimal Models ◽  
Continuum Approach ◽  
Point Correlation ◽  
Local Operators ◽  
The One ◽  
The Continuum

The tree-level three-point correlation functions of local operators in the general (p, q) minimal models coupled to gravity are calculated in the continuum approach. On one hand, the result agrees with the unitary series (q=p+1); and on the other hand, for p=2, q=2k−1, we find agreement with the one-matrix model results.

scholarly journals Rescaling Ward Identities in the Random Normal Matrix Model

2018 ◽  
Vol 50 (1) ◽  
pp. 63-127 ◽  
Author(s):  
Yacin Ameur ◽  
Nam-Gyu Kang ◽  
Nikolai Makarov
Keyword(s):  
Matrix Model ◽  
Normal Matrix ◽  
Ward Identities
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