T-duality building blocks for ${\ensuremath{\alpha}}^{\ensuremath{'}}$ string corrections

Open Access

T-duality building blocks for $α^{'}$ string corrections

Marina David and James T. Liu

Phys. Rev. D 107, 046008 – Published 15 February 2023

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 $α^{'}$ 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 $α^{'}$ . We also comment on the four-point functions for corrections of order $α^{' 3}$ in the type II string.

Received 1 December 2022
Accepted 7 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.046008

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Published by the American Physical Society