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

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.

💡 Research Summary

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The paper investigates the fate of the gravitational Green‑Schwarz (GS) transformation in the non‑relativistic (NR) limit of ten‑dimensional heterotic supergravity when four‑derivative α′ corrections are present. In the relativistic theory the Kalb‑Ramond two‑form Bμν transforms non‑covariantly under local Lorentz rotations because of Chern‑Simons (CS) couplings to the spin connection; this transformation is essential for the cancellation of mixed gauge‑gravitational anomalies. The authors ask whether this mechanism survives when the theory is taken to a NR regime, a limit that has become increasingly important in the study of Newton‑Cartan geometry, non‑Lorentzian string backgrounds, and duality‑invariant formulations.

The analysis begins by reviewing the α′‑corrected heterotic action, which includes curvature‑squared terms and a CS modification of the three‑form field strength H = dB + α′ Ω₃ (Ω₃ being the Lorentz CS three‑form). The GS variation of B is δΛBμν = −½ α′ ∂