Higher derivative heterotic supergravity on a torus and supersymmetry

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.