Higher derivative heterotic supergravity on a torus and supersymmetry

TL;DR

This paper studies the reduction of heterotic supergravity on a torus, revealing an $O(d,d)$ symmetry at higher derivative order and analyzing the interplay between gravity and vector multiplets beyond leading order.

Contribution

It explicitly reduces four-derivative heterotic supergravity and its supersymmetry variations, demonstrating manifest $O(d)_- imes O(d)_+$ invariance after field redefinitions.

Findings

The reduced theory exhibits a continuous $O(d,d)$ symmetry at all perturbative orders.

The action and supersymmetry variations are explicitly invariant under $O(d)_- imes O(d)_+$.

The analysis clarifies the interaction between gravity and vector multiplets beyond leading order.

Abstract

Ignoring ten-dimensional heterotic gauge fields, heterotic supergravity reduced on a $d$-dimensional torus gives rise to a half-maximal supergravity coupled to $d$ vector multiplets. The reduced theory has a continuous $O(d,d;\mathbb R)/O(d)_-\times O(d)_+$ symmetry that persists to all perturbative orders in the string $\alpha'$ expansion. We highlight this symmetry by explicitly reducing the bosonic sector of four-derivative heterotic supergravity as well as its fermionic supersymmetry variations. After appropriate field redefinitions, the resulting action and supersymmetry variations are manifestly $O(d)_-\times O(d)_+$ invariant. This reduction allows us to explore the interplay between the gravity and vector multiplets beyond leading order, where (in our conventions) $O(d)_-$ is the supergravity R-symmetry while $O(d)_+$ is a flavor symmetry of the $d$ vector multiplets.