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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{moore2026comment,
  title = {{A Comment On Topological Degeneracy In Gauged WZW Models}},
  author = {Gregory W. Moore and Eliezer Rabinovici and Ranveer Kumar Singh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.11308},
  eprint = {2608.11308},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.11308},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Comment On Topological Degeneracy In Gauged WZW Models
AU  - Gregory W. Moore
AU  - Eliezer Rabinovici
AU  - Ranveer Kumar Singh
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2608.11308
UR  - https://arxiv.org/abs/2608.11308
AB  - 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.
ER  -