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S-duality in higher-derivative corrections of heterotic supergravity

Mohammad R. Garousi

TL;DR

The paper shows that maintaining T-duality in heterotic supergravity with a Green–Schwarz–deformed B-field requires an infinite tower of covariant higher-derivative terms, all scaling as $e^{-2Φ}$. It proves that the S-duality between heterotic and Type I receives no higher-derivative corrections, enabling the exact transfer of α'–order couplings to Type I in a dilaton-derivative–free scheme, and derives the explicit Type I action at order α'. Furthermore, it uses a six-dimensional heterotic–Type IIA duality via K3 to test and corroborate the T-duality–predicted NS-NS couplings in Type II, showing that the sphere-level α'-couplings do not survive after appropriate field redefinitions. Together, these results establish a robust, duality-consistent framework for higher-derivative corrections across heterotic, Type I, and Type II theories and point to concrete directions for further checks, including disk-level calculations and T-duality to Type I' theories. The work advances understanding of how exact dualities constrain and determine higher-derivative structures in string effective actions, with implications for non-perturbative completions and cross-theory consistency checks.

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 $e^{-2Φ}$. Within this tower, the couplings at orders $α'$ and $α'^2$ 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 $α'$ in a scheme that omits dilaton derivatives.

S-duality in higher-derivative corrections of heterotic supergravity

TL;DR

The paper shows that maintaining T-duality in heterotic supergravity with a Green–Schwarz–deformed B-field requires an infinite tower of covariant higher-derivative terms, all scaling as . It proves that the S-duality between heterotic and Type I receives no higher-derivative corrections, enabling the exact transfer of α'–order couplings to Type I in a dilaton-derivative–free scheme, and derives the explicit Type I action at order α'. Furthermore, it uses a six-dimensional heterotic–Type IIA duality via K3 to test and corroborate the T-duality–predicted NS-NS couplings in Type II, showing that the sphere-level α'-couplings do not survive after appropriate field redefinitions. Together, these results establish a robust, duality-consistent framework for higher-derivative corrections across heterotic, Type I, and Type II theories and point to concrete directions for further checks, including disk-level calculations and T-duality to Type I' theories. The work advances understanding of how exact dualities constrain and determine higher-derivative structures in string effective actions, with implications for non-perturbative completions and cross-theory consistency checks.

Abstract

This study examines the consistency of heterotic supergravity under T-duality when the -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 . Within this tower, the couplings at orders and 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 in a scheme that omits dilaton derivatives.

Paper Structure

This paper contains 4 sections, 26 equations.

Table of Contents

  1. Introduction
  2. Heterotic/Type I duality
  3. Six-dimensional Heterotic/Type IIA duality
  4. Discussion