Trivialization of the gravitational Green-Schwarz transformation in the non-relativistic limit of string theory

TL;DR

This paper demonstrates that the gravitational Green-Schwarz transformation becomes trivial in the non-relativistic limit of heterotic supergravity, simplifying anomaly cancellation and advancing understanding of string theory limits.

Contribution

It explicitly shows the trivialization of the gravitational Green-Schwarz transformation in the non-relativistic limit and constructs a field redefinition that makes the two-form invariant.

Findings

Green-Schwarz transformation becomes trivial in the NR limit

Constructed a field redefinition making the two-form invariant

Chern-Simons terms are exact and lead to trivial Bianchi identity

Abstract

We show that the gravitational Green-Schwarz (GS) transformation becomes trivial in the non-relativistic (NR) limit of ten-dimensional heterotic supergravity with four-derivative corrections. This constitutes an important step towards establishing the trivialization of the GS mechanism in this limit. In this work, we perform a NR expansion of the Kalb-Ramond field and identify the finite Green-Schwarz transformation in this limit, which can be interpreted as a non-covariant $SO(8)$ transformation. We then construct an explicit field redefinition such that the redefined two-form is invariant under this symmetry. This result is compared with the previously reported trivialization of the gauge GS mechanism under the same limit. Both field redefinitions can be implemented simultaneously, and the associated Chern-Simons terms are exact, arising directly from the redefinition structure, and leading to a trivial Bianchi identity. These results support the expectation that anomaly cancellation becomes automatic in the NR regime, and therefore we discuss their potential implications.