S-duality in higher-derivative corrections of heterotic supergravity

Abstract: This study investigates the consistency of heterotic supergravity, where the $B$-field gauge transformation becomes anomalous due to the Green-Schwarz mechanism, under T-duality transformations. We establish that preserving T-duality necessitates an infinite tower of higher-derivative couplings proportional to $e^{-2\Phi}$. For spacetimes featuring a Killing self-dual circle, these couplings remain immune to quantum corrections. Leveraging S-duality in heterotic/type I string theory, we then identify the corresponding couplings in type I theory. Notably, our analysis reveals that standard S-duality transformations do not involve higher-derivative corrections. Moreover, field redefinitions in heterotic theory do not typically correspond directly, under S-duality, to analogous field redefinitions in type I theory, and vice versa. Building on these insights, we derive the explicit form of the effective action for type I theory at the $\alpha'$ order, adhering to a scheme that omits derivatives of the dilaton.