An Introduction to T-Duality in String Theory

TL;DR

This paper provides a comprehensive introduction to T-duality in string theory, covering abelian and non-abelian cases, and discusses its implications for cosmology and the concept of distance.

Contribution

It reviews existing approaches to T-duality, clarifies Buscher's dilaton transformation, and explores the relation of duality to canonical transformations and cosmological implications.

Findings

Buscher's dilaton transformation derived from gauge measure

Duality understood as a canonical transformation

Implications for cosmological constant and distance in string theory

Abstract

In these lectures a general introduction to T-duality is given. In the abelian case the approaches of Buscher, and Ro\u{c}ek and Verlinde are reviewed. Buscher's prescription for the dilaton transformation is recovered from a careful definition of the gauge integration measure. It is also shown how duality can be understood as a quite simple canonical transformation. Some aspects of non-abelian duality are also discussed, in particular what is known on relation to canonical transformations. Some implications of the existence of duality on the cosmological constant and the definition of distance in String Theory are also suggested.