On Nonabelian Duality

TL;DR

This paper clarifies that nonabelian duality acts as a symmetry between different conformal field theories rather than within a single theory, revealing a nonlocal symmetry and providing methods to find inverse duals with new examples.

Contribution

It demonstrates that nonabelian duality is a theory-to-theory symmetry, introduces a nonlocal symmetry in dual theories, and presents new examples and inverse dual transformations.

Findings

Nonabelian duality is not a symmetry of a single theory.

A nonlocal symmetry exists in nonabelian dual theories.

Methods to find inverse dual transformations are developed.

Abstract

We show that nonabelian duality is not a symmetry of a conformal field theory, but rather a symmetry between different theories. We expose a nonlocal symmetry of nonabelian dual theories. We show how, in the case with vanishing isotropy, it can be used to find the inverse dual transformation. Finally, we consider a number of new examples.