Gravitational four-derivative corrections in non-relativistic heterotic supergravity and the $SO(8)$ Green-Schwarz mechanism

Abstract

We present the first explicit construction of the four-derivative gravitational corrections to heterotic supergravity in the non-relativistic (NR) limit. By extending the Bergshoeff-de Roo identification to NR backgrounds, we obtain the full finite four-derivative completion of the gravitational sector of the NR heterotic supergravity action. A key outcome is the emergence of a gravitational $SO(8)$ Green-Schwarz mechanism from the NR gauge transformation of the Kalb-Ramond field. This mechanism can be trivialized through suitable field redefinitions, in agreement with a previous analysis of this transformation. Our results establish a systematic framework for incorporating higher-curvature gravitational dynamics into NR string heterotic backgrounds.