A Note on T-duality in Heterotic String Theory

TL;DR

This paper revisits T-duality in heterotic string theory, revealing modifications due to world-sheet chirality that affect standard transformation rules and ensure correct Bianchi identities in dual models.

Contribution

It identifies the need for modified T-duality rules in heterotic string theory, especially for curved backgrounds, and derives new rules consistent with Bianchi identities.

Findings

Standard T-duality rules are incorrect for curved backgrounds.

Modified T-duality rules ensure correct Bianchi identities.

Explicit examples demonstrate the validity of new rules.

Abstract

We revisit the T-duality transformation rules in heterotic string theory, pointing out that the chiral structure of the world-sheet leads to a modification of the standard Buscher's transformation rules. The simplest instance of such modifications arises for toroidal compactifications, which are rederived by analyzing a bosonized version of the heterotic world-sheet Lagrangian. Our study indicates that the usual heterotic toroidal T-duality rules naively extended to the curved case cannot be correct, leading in particular to an incorrect Bianchi identity for the field strength H of the Kalb-Ramond field B. We explicitly show this problem and provide a specific example of dual models where we are able to get new T-duality rules which, contrary to the standard ones, lead to a correct T-dual Bianchi identity for H to all orders in \alpha'.