Related papers: Large-N Gauge Theories
It is generally known for $\mathrm{U}(N)$ gauge theory at finite temperature that phase transitions are manifested by taking the large-$N$ limit. Since the large-$N$ theory undergoes two thermodynamic phase transitions, a nontrivial…
These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly $\su$. We give detailed examples, develop the…
Condensed account of the Lectures delivered at the Meeting on {\it Noncommutative Geometry in Field and String Theory}, Corfu, September 18 - 20, 2005.
These are notes for four lectures on higher structures in M-theory as presented at workshops at the Erwin Schroedinger Institute and Tohoku University. The first lecture gives an overview of systems of multiple M5-branes and introduces the…
This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic…
These notes are based on lectures given in Valencia in October 2008 and in Stockholm in November 2008, in the framework of the Nordita workshop "Geometrical aspects of String Theory". We introduce the notion of a metric 3-Lie algebra and…
The partition function of a two-dimensional quantum gauge theory in the large-$N$ limit is expressed as the functional integral over some scalar field. The large-$N$ saddle point equation is presented and solved. The free energy is…
This article gives details of the course on "Quantum Matter in optical lattices and high-Q cavities" given at the School of Physics XXVIII at UNAM in 2021. The notes describe useful concepts for analog quantum simulation and details of…
The different large $N$ limits of supersymmetric quantum field theories in three, four, and five dimensions are reviewed. We distinguish between the planar limit of SQCD theories, the M-theory limit suited in three and five dimensions, and…
CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…
We construct the six dimensional Quantum Chromodynamics (QCD) Lagrangian in a linear covariant gauge and subsequently renormalize it at two loops in the MSbar scheme. The coupling constant corresponding to the gauge interaction is…
We study numerically various wave functions in a gauged matrix quantum mechanics of six commuting hermitian $N\times N$ matrices. Our simulations span ranges of $N$ up to 10000. This system is a truncated and quenched version of N=4 SYM…
Lectures given at International School of Physics ``Enrico Fermi'', Varenna, Villa Monastero, June 28-July 7 1994
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…
This paper consists of two (still only vaguely) related parts: in the first, we briefly review work done in the past three years on the ``planar equivalence" between a class of non-supersymmetric theories (including limiting cases of QCD)…
In this talk I will first give a short discussion of some lattice results for QCD at finite temperature. I will then describe in some detail the technique of dimensional reduction, which in principle is a powerful technique to obtain…
After receiving many requests for reprints of this article, describing the original ideas on the quark gluon gauge theory, which we later named QCD, we decided to place the article in the e-Print archive.
We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional N=1 supersymmetric SU(N) gauge theory with one adjoint and a pair of…
I review some recent works on the Hermitean one-matrix and d-dimensional gauge-invariant matrix models. Special attention is paid to solving the models at large-N by the loop equations. For the one-matrix model the main result concerns…
It was shown in arXiv:0912.1456 that the large-$N$ reduction holds on group manifolds in the sense that a large-$N$ gauge theory on a group manifold is realized by a matrix model which is obtained by dimensionally reducing the original…