scholarly journals Lectures on non-perturbative effects in large N gauge theories, matrix models and strings

2014 ◽  
Vol 62 (5-6) ◽  
pp. 455-540 ◽  
Author(s):  
M. Mariño
Keyword(s):  
Matrix Models ◽  
Gauge Theories ◽  
Large N

scholarly journals LARGE N REDUCTION ON GROUP MANIFOLDS

2010 ◽  
Vol 25 (17) ◽  
pp. 3389-3406 ◽  
Author(s):  
HIKARU KAWAI ◽  
SHINJI SHIMASAKI ◽  
ASATO TSUCHIYA
Keyword(s):  
Matrix Models ◽  
Gauge Theories ◽  
Field Theories ◽  
Gauge Invariant ◽  
Large N

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S3 can be regularized in a gauge invariant and SO(4) invariant manner.

scholarly journals AN INTRODUCTION TO SUPERSYMMETRIC GAUGE THEORIES AND MATRIX MODELS

2004 ◽  
Vol 19 (13) ◽  
pp. 2015-2078 ◽  
Author(s):  
RICCARDO ARGURIO ◽  
GABRIELE FERRETTI ◽  
RAINER HEISE
Keyword(s):  
Matrix Models ◽  
Gauge Theories ◽  
Supersymmetric Gauge Theories ◽  
Large N ◽  
Chiral Ring ◽  
Supersymmetric Gauge ◽  
The One

We give an introduction to the recently-established connection between supersymmetric gauge theories and matrix models. We begin by reviewing previous material that is required in order to follow the latest developments. This includes the superfield formulation of gauge theories, holomorphy, the chiral ring, the Konishi anomaly and the large N limit. We then present both the diagrammatic proof of the connection and the one based on the anomaly. Our discussion is entirely field theoretical and self contained.

scholarly journals Fermionic Matrix Models

1997 ◽  
Vol 12 (12) ◽  
pp. 2135-2291 ◽  
Author(s):  
Gordon W. Semenoff ◽  
Richard J. Szabo
Keyword(s):  
String Theory ◽  
Matrix Models ◽  
Degrees Of Freedom ◽  
Integrable Hierarchies ◽  
Gauge Theories ◽  
Target Space ◽  
Vector Model ◽  
Convergence Properties ◽  
Random Surface ◽  
Large N

We review a class of matrix models whose degrees of freedom are matrices with anti-commuting elements. We discuss the properties of the adjoint fermion one-matrix, two-matrix and gauge-invariant D-dimensional matrix models at large N and compare them with their bosonic counterparts, which are the more familiar Hermitian matrix models. We derive and solve the complete sets of loop equations for the correlators of these models and use these equations to examine critical behavior. The topological large N expansions are also constructed and their relation to other aspects of modern string theory, such as integrable hierarchies, is discussed. We use these connections to discuss the applications of these matrix models to string theory and induced gauge theories. We argue that as such the fermionic matrix models may provide a novel generalization of the discretized random surface representation of quantum gravity in which the genus sum alternates and the sums over genera for correlators have better convergence properties than their Hermitian counterparts. We discuss the use of adjoint fermions instead of adjoint scalars to study induced gauge theories. We also discuss two classes of dimensionally reduced models, a fermionic vector model and a supersymmetric matrix model, and discuss their applications to the branched polymer phase of string theories in target space dimensions D > 1 and also to the meander problem.

scholarly journals Quantum information probes of charge fractionalization in large-N gauge theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Brandon S. DiNunno ◽  
Niko Jokela ◽  
Juan F. Pedraza ◽  
Arttu Pönni
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
Strongly Coupled ◽  
Information Theoretic ◽  
Large N ◽  
Wide Range ◽  
Charge Fractionalization ◽  
Electric Flux

Abstract We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

scholarly journals Casimir scaling and renormalization of Polyakov loops in large-N gauge theories

2012 ◽  
Vol 2012 (5) ◽  
Author(s):  
Anne Mykkänen ◽  
Marco Panero ◽  
Kari Rummukainen
Keyword(s):  
Gauge Theories ◽  
Large N ◽  
Polyakov Loops

PHASE DIAGRAM AND ORTHOGONAL POLYNOMIALS IN MULTIPLE-WELL MATRIX MODELS

1991 ◽  
Vol 06 (25) ◽  
pp. 4491-4515 ◽  
Author(s):  
OLAF LECHTENFELD ◽  
RASHMI RAY ◽  
ARUP RAY
Keyword(s):  
Phase Diagram ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Matrix Model ◽  
Phase Structure ◽  
Saddle Points ◽  
Tree Level ◽  
Potential Wells ◽  
Large N

We investigate a zero-dimensional Hermitian one-matrix model in a triple-well potential. Its tree-level phase structure is analyzed semiclassically as well as in the framework of orthogonal polynomials. Some multiple-arc eigenvalue distributions in the first method correspond to quasiperiodic large-N behavior of recursion coefficients for the second. We further establish this connection between the two approaches by finding three-arc saddle points from orthogonal polynomials. The latter require a modification for nondegenerate potential minima; we propose weighing the average over potential wells.

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