A Note on T-Duality, Open Strings in B-field Background and Canonical Transformations

TL;DR

This paper explores how T-duality for open strings with B-field backgrounds can be understood through canonical transformations, specifically showing that certain modular transformations are a subset of these transformations.

Contribution

It demonstrates that T-duality transformations for open strings with B-fields can be realized as canonical transformations, linking string dualities with classical mechanics concepts.

Findings

T-duality for open strings can be described via canonical transformations.

SL(2,Z) transformations are a subset of these canonical transformations.

The approach applies to type II strings on a two-torus.

Abstract

In this paper we study T-duality for open strings ending on branes with non-zero B-field on them from the point of view of canonical transformations. For the particular case of type II strings on the two torus we show that the $Sl(2,Z)_N$ transformations can be understood as a sub-class of canonical transformations on the open strings in the B-field background.