Higher derivative heterotic supergravity on a torus and supersymmetry

A bstract 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 ; ℝ )/ O ( d ) − × O ( d ) + symmetry that persists to all perturbative orders in the string α ′ 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 ) − × 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.