S-duality in higher-derivative corrections of heterotic supergravity

TL;DR

This paper investigates how T-duality constrains higher-derivative corrections in heterotic supergravity, showing that certain couplings are protected from quantum corrections and confirming the invariance of S-duality, leading to explicit effective action forms.

Contribution

It demonstrates that T-duality invariance requires an infinite tower of higher-derivative couplings and confirms the unmodified nature of S-duality at higher orders.

Findings

Higher-derivative couplings scale as e^{-2Φ}

Couplings at orders α' and α'^2 are quantum correction protected

Explicit form of type I effective action at order α' derived

Abstract

This study examines the consistency of heterotic supergravity under T-duality when the $B$-field gauge transformation is rendered anomalous by the Green-Schwarz mechanism. We demonstrate that T-duality invariance mandates an infinite tower of higher-derivative couplings, all scaling as $e^{-2\Phi}$. Within this tower, the couplings at orders $\alpha'$ and $\alpha'^2$ are protected from quantum corrections, making them exact and therefore amenable to analysis under the S-duality between heterotic and type I string theory. Our results confirm that the standard S-duality map itself does not receive higher-derivative modifications. Leveraging this exact correspondence, we derive the explicit form of the type I effective action at order $\alpha'$ in a scheme that omits dilaton derivatives.