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arXiv · 2608.11308

A Comment On Topological Degeneracy In Gauged WZW Models

Gregory W. Moore·Eliezer Rabinovici·Ranveer Kumar Singh
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Abstract

Given a Lie group $G$, a level $k$, and a Lie subgroup $H$ one can construct 2d conformal field theories by either 1.) gauging a nonanomalous $H$ symmetry of the WZW model constructed from $(G,k)$ or 2.) using an algebraic procedure known as the GKO coset construction. The two models are closely related, but not precisely the same: The gauged WZW model is identified with the corresponding GKO model coupled to a 2d topological field theory. The topological theory is characterized by a commutative Frobenius algebra derived from the endomorphisms of an algebra object in a modular tensor category constructed from $(G,H,k)$. The partition function on the torus of the two models differ by a factor of the dimension of this algebra of endomorphisms. Concrete examples are constructed and some applications to string theory and 2d Yang-Mills coupled to nonanomalous matter are briefly discussed. This paper is a summary of a longer companion paper.

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Gregory W. Moore, Eliezer Rabinovici, Ranveer Kumar Singh. 2026-08-11. A Comment On Topological Degeneracy In Gauged WZW Models. https://arxiv.org/abs/2608.11308

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