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

TL;DR

The paper investigates whether Green-Schwarz anomaly cancellation persists in the non-relativistic (NR) limit of ten-dimensional heterotic supergravity with $oldsymbol{ abla}^4$-type corrections. By performing a NR expansion and applying a rescaling $oldsymbol{rac{oldsymbol{\alpha' o oldsymbol{\alpha'_{ ext{NR}}/oldsymbol{c^2}}}}}$, the authors construct an explicit field redefinition $ ilde{b}_{\\mu\nu}$ that trivializes the gravitational GS transformation, yielding a finite, $SO(8)$ covariant 3-form curvature $ar{h}_{\mu\nu\rho}$ that becomes exact. They compare this with the gauge GS trivialization and show that both can be made simultaneously trivial, implying a potential automatic anomaly cancellation in the NR regime and allowing broader gauge structures and compactifications. The work also discusses implications for Wald entropy, the first law in NR backgrounds, and potential connections to duality-invariant frameworks such as Double Field Theory (DFT). Overall, the results point to a new paradigm where anomaly-related consistency conditions may be relaxed in NR heterotic theories, with several avenues for future exploration including supersymmetry, NR DFT, and higher-derivative completions.

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.