Conformal Field Theory Techniques for Large N Group Theory
Abstract
We show how to use quantum mechanics on the group manifold U(N) as a tool for problems in U(N) representation theory. The quantum mechanics reduces to free fermions on the circle, which in the large N limit become relativistic. The theory can be bosonized giving the Das-Jevicki-Sakita collective field theory. The formalism is particularly suited to problems involving tensor product multiplicity (Littlewood-Richardson) coefficients. As examples, we discuss the partition function of two-dimensional Yang-Mills theory on the sphere, and the zero magnetic field limit of D-dimensional Eguchi-Kawai Yang-Mills theory. We give the leading O(N^0) solution of the latter theory, using a method which allows computing corrections. Largely (but not completely) superseded by hep-th/9311130.
Cite
@article{arxiv.hep-th/9303159,
title = {Conformal Field Theory Techniques for Large N Group Theory},
author = {Michael R. Douglas},
journal= {arXiv preprint arXiv:hep-th/9303159},
year = {2007}
}
Comments
RU-93-13, NSF-ITP-93-39, 13 pp