T-duality building blocks for $\alpha'$ string corrections

TL;DR

This paper explores how T-duality constrains higher derivative corrections in string theory, providing new formulations for invariants and analyzing specific string actions at order ' and four-point functions at order '^3.

Contribution

It introduces a new approach to express $O(d,d)$ invariants using linear combinations of metric and B-field, enhancing understanding of ' corrections under T-duality.

Findings

Reformulation of $O(d,d)$ invariants in terms of metric and B-field.

Analysis of heterotic and bosonic string actions at order '.

Comments on four-point functions at order '^3 in type II string.

Abstract

T-duality has been shown to constrain the higher derivative corrections of string theory. We revisit the problem of understanding the T-duality constraints imposed on the $\alpha'$ corrections using the language of a torsionful connection. We find a convenient way to express the $O(d,d)$ invariants in terms of linear combinations of the metric and B-field for general $d$-dimensional torus compactifications, which we then use to revisit the heterotic and bosonic ten-dimensional string action at order $\alpha'$. We also comment on the four-point functions for corrections of order $\alpha'^3$ in the type II string.