Notes on gauging noneffective group actions

TL;DR

This paper explores gauged sigma models with noneffective group actions, revealing nonperturbative effects and new conformal field theory presentations involving fields valued in roots of unity.

Contribution

It provides a detailed analysis of nonperturbative phenomena in gauged sigma models with noneffective groups, introducing novel CFT descriptions.

Findings

Nonperturbative effects distinguish noneffective from effective gauged models.

Deformations along twisted sector moduli lead to new CFT presentations.

Fields valued in roots of unity characterize these new conformal theories.

Abstract

In this paper we study sigma models in which a noneffective group action has been gauged. Such gauged sigma models turn out to be different from gauged sigma models in which an effectively-acting group is gauged, because of nonperturbative effects on the worldsheet. We concentrate on finite noneffectively-acting groups, though we also outline how analogous phenomena also happen in nonfinite noneffectively-acting groups. We find that understanding deformations along twisted sector moduli in these theories leads one to new presentations of CFT's, defined by fields valued in roots of unity.