Duality, Quotients, and Currents

TL;DR

This paper explores the extension of $R o 1/R$ duality to a broad class of conformally invariant sigma models with isometries, revealing their structure as quotients of a self-dual model and clarifying the duality's role as a symmetry.

Contribution

It demonstrates that dual sigma models can be viewed as quotients of a self-dual model, extending the duality concept to supersymmetric models and clarifying its interpretation in conformal field theory.

Findings

Dual sigma models are quotients of a self-dual model.

The duality acts as a symmetry in conformal field theory.

Results extend to $N=2$ supersymmetric sigma models.

Abstract

We study the generalization of $R\to 1/R$ duality to arbitrary conformally invariant sigma models with an isometry. We show that any pair of dual sigma models can be represented as quotients of a self-dual sigma model obtained by gauging different combinations of chiral currents. This observation is used to clarify the interpretation of the generalized duality as a symmetry of conformal field theory. We extend these results to $N=2$ supersymmetric sigma models.