Some Global Aspects of Duality is String Theory

TL;DR

This paper investigates the global properties of duality transformations in String Theory and Field Theory, focusing on their effects on topology, the partition function, and the cosmological constant, including examples of non-abelian duality.

Contribution

It provides a detailed analysis of duality equivalences at the topological and operator levels, and constructs a non-abelian dual of SL(2,R) as a three-dimensional black hole.

Findings

Dual models with different topologies are equivalent at the partition function level.

The behavior of the cosmological constant under duality transformations is characterized.

A non-abelian dual of SL(2,R) is constructed, representing a 3D black hole.

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