The T-dual symmetries of a bosonic string

TL;DR

This paper explores how T-duality relates symmetry transformations in bosonic string theories, showing that certain symmetries are exchanged under T-duality, including general coordinate and gauge transformations.

Contribution

It demonstrates that T-duality connects symmetry transformations of bosonic strings, revealing that these symmetries are exchanged between the original and T-dual theories.

Findings

Symmetry transformations are T-dual to each other.

General coordinate and gauge transformations are exchanged under T-duality.

T-duality preserves the conformal invariance of the string theory.

Abstract

We investigate whether the symmetry transformations of a bosonic string are connected by T-duality. We start with a standard closed string theory. We continue with a modified open string theory, modified to preserve the symmetry transformations possessed by the closed string theory. Because the string theory is conformally invariant world sheet field theory, in order to find the transformations which preserve the physics, one has to demand the isomorphism between the conformal field theories corresponding to the initial and the transformed field configurations. We find the symmetry transformations corresponding to the similarity transformation of the energy-momentum tensor, and find that their generators are T-dual. Particularly, we find that the general coordinate and local gauge transformations are T-dual, so we conclude that T-duality in addition to the well known exchanges, transforms symmetries of the initial and its T-dual theory into each other.