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WZW branes and gerbes

Krzysztof Gawedzki, Nuno Reis

Abstract

We reconsider the role that bundle gerbes play in the formulation of the WZW model on closed and open surfaces. In particular, we show how an analysis of bundle gerbes on groups covered by SU(N) permits to determine the spectrum of symmetric branes in the boundary version of the WZW model with such groups as the target. We also describe a simple relation between the open string amplitudes in the WZW models based on simply connected groups and in their simple-current orbifolds.

WZW branes and gerbes

Abstract

We reconsider the role that bundle gerbes play in the formulation of the WZW model on closed and open surfaces. In particular, we show how an analysis of bundle gerbes on groups covered by SU(N) permits to determine the spectrum of symmetric branes in the boundary version of the WZW model with such groups as the target. We also describe a simple relation between the open string amplitudes in the WZW models based on simply connected groups and in their simple-current orbifolds.

Paper Structure

This paper contains 21 sections, 258 equations.

Table of Contents

  1. Introduction
  2. Topological action functionals and gerbes
  3. Dirac monopoles and line bundles
  4. Topological actions in two-dimensional field theories
  5. Bundle gerbes with connections
  6. Gerbes on groups $SU(N)$
  7. Gerbes on groups covered by $SU(N)$
  8. Gerbes on discrete quotients
  9. Bundle gerbes and loop-space line bundles
  10. Gerbes and branes
  11. Branes in the WZW model
  12. $SU(N)$ groups
  13. Groups covered by $SU(N)$
  14. Partition functions
  15. Bulk case
  16. ...and 6 more sections