No manifest T-duality at order $\alpha'^3$

TL;DR

The paper demonstrates that at order ^3, the expected manifest T-duality symmetry cannot be maintained in ten-dimensional string theory, challenging approaches that rely on this symmetry for a complete description.

Contribution

It provides explicit field redefinitions at order ^3 and shows they cannot be extended to ten dimensions, questioning the validity of manifest T-duality formulations.

Findings

Manifest T-duality invariance fails at order ^3 in ten dimensions.

Field redefinitions at this order cannot be lifted to ten dimensions.

Challenges the use of generalized geometry for a complete string theory description.

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 $\alpha'^3$ 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.