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On Nonabelian Duality

Amit Giveon, Martin Rocek

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.

On Nonabelian Duality

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.

Paper Structure

This paper contains 12 sections, 61 equations.

Table of Contents

  1. Introduction
  2. Review of Abelian Duality
  3. General Aspects of Nonabelian Duality
  4. The case without isotropy
  5. The original model.
  6. The dual model.
  7. Some comments on the duality group.
  8. An example without isotropy
  9. The $G$-dual of the $G$-WZNW model: An example with isotropy
  10. General discussion
  11. The $SU(2)$ example
  12. Comments and Discussion