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arXiv · hep-th/9303159

Conformal Field Theory Techniques for Large N Group Theory

Michael R. Douglas
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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 Largely (but not completely) superseded by hep-th/9311130.

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Michael R. Douglas. 1993-03-30. Conformal Field Theory Techniques for Large N Group Theory. https://arxiv.org/abs/hep-th/9303159

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