T-Duality in Arbitrary String Backgrounds

TL;DR

This paper presents a new, general method to understand T-Duality in string theory, extending its applicability beyond symmetric backgrounds and clarifying its local nature, with explicit examples and transformation rules.

Contribution

It introduces a simple, powerful approach to T-Duality transformations applicable to arbitrary backgrounds, including those without symmetries, and clarifies misconceptions about non-locality.

Findings

Rederived known T-Duality transformations

Proved non-locality is an illusion in these transformations

Provided explicit example of metric transformation without Killing symmetries

Abstract

T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus are inverted. Even in this case, however, conventional techniques permit an understanding of the transformations only in the case where the metric on the torus is endowed with Abelian Killing symmetries. Attempting to apply these techniques to a general metric appears to yield a non-local world-sheet theory that would defy interpretation in terms of space-time fields. However, there is now available a simple but powerful general approach to understanding the symmetry transformations of string theory, which are generated by certain similarity transformations of the stress-tensors of the associated conformal field theories. We apply this method to the particular case of T-Duality and i) rederive the known transformations, ii) prove that the problem of non-locality is illusory, iii) give an explicit example of the transformation of a metric that lacks Killing symmetries and iv) derive a simple transformation rule for arbitrary string fields on tori.