No manifest T-duality at order $\hat{I}{\pm }^{\prime 3}$

Abstract

When reduced from $10$ to $10-d$ dimensions tree-level string theory exhibits an $O(d,d)$ symmetry. This symmetry, which is closely related to T-duality, appears only after certain field redefinitions. We find a simple form for a subset of these redefinitions at order $\hat{I}{\pm }^{\prime 3}$ and show that they cannot be lifted to ten dimensions. This is inconsistent with ``manifestly T-duality invariant'' approaches such as generalized geometry (in the uncompactified setting). Such formulations therefore seem not to be the correct language to describe string theory.

7 pages; v2: Clarifications regarding total derivative terms and corrections to transformations. Published version