Some Global Aspects of Duality is String Theory

TL;DR

The paper investigates global/topological facets of duality in string theory, detailing how abelian and non-abelian dualities can relate theories on different geometries and topologies. It develops a covariant gauging framework to implement duality, recovers Buscher transforms, and demonstrates generic topology changes (e.g., S^3 to S^2 imes S^1) with explicit WZW analyses. It also delivers an operator-mapping (order-disorder) dictionary and examines the behavior of the cosmological constant under duality, highlighting both invariance at leading order and subtle changes in curvature/dilaton sectors. In the non-abelian sector, the work presents intriguing results such as an AdS black-hole–like space arising from SL(2,R) duality, but also candidly discusses significant obstacles (global/topological issues and operator mappings) that prevent a simple, universal non-abelian duality symmetry from emerging.

Abstract

We explore some of the global aspects of duality transformations in String Theory and Field Theory. We analyze in some detail the equivalence of dual models corresponding to different topologies at the level of the partition function and in terms of the operator correspondence for abelian duality. We analyze the behavior of the cosmological constant under these transformations. We also explore several examples of non-abelian duality where the classical background interpretation can be maintained for the original and the dual theories. In particular we construct a non-abelian dual of $SL(2,R)$ which turns out to be a three-dimensional black hole

Figures (1)

• Figure 1: Fig.1: Penrose diagram for ${\tilde{M}}$.