A note on T-duality in heterotic string theory

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 α'