Notes on gauging noneffective group actions

TL;DR

This paper investigates gauged sigma models in which a group acts noneffectively, showing that such gaugings are physically distinct from gauging the effectively-acting quotient due to worldsheet nonperturbative effects. It develops the massless-spectrum framework for noneffective orbifolds, revealing that twisted sectors correspond to conjugacy classes but can exhibit nontrivial multiplicities, and introduces twist fields that are effectively described by fields valued in roots of unity. The work connects these theories to gerbes and Calabi–Yau stacks, discusses deformation theory and mirror symmetry in this context, and analyzes D-branes and quantum symmetries within noneffective orbifolds. It also highlights a false lead that omits certain twisted sectors, ultimately demonstrating that full sector inclusion preserves unitarity and modular invariance. Overall, the paper lays groundwork for understanding universality classes of gauged sigma models and their mathematical interpretation via stacks and gerbes, with implications for future GLSM formulations on stacks and their mirrors.

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.

Figures (3)

• Figure 1: The four two-torsion points on an elliptic curve.
• Figure 2: An annulus diagram, interpreted in two ways
• Figure 3: An annulus diagram in an orbifold