The non-relativistic limit of HSZ Theory

TL;DR

This work analyzes the non-relativistic limit of HSZ theory, a finite, T-duality–invariant higher-derivative gravity model formulated in double field theory. It shows the NR Lagrangian remains finite to all orders and derives three-derivative corrections to symmetry transformations alongside four-derivative b-field contributions. Unlike the relativistic case, NR corrections to the metric cannot be fully removed by field redefinitions, signaling Green-Schwarz–like deformations of diffeomorphisms in the NR regime. Since HSZ interpolates between heterotic and bosonic strings, the NR results provide a truncation of the heterotic four-derivative supergravity structure in the NR limit, with preNR field redefinitions playing a crucial role for a consistent reduction.

Abstract

We study the non-relativistic (NR) limit of HSZ theory, a higher-derivative theory of gravity with exact and manifest T-duality invariance. Since the theory can be formulated using the generalized metric formalism, the HSZ Lagrangian remains convergent to all orders in derivatives when taking the NR limit. In this work, we analyze the three-derivative corrections to the symmetry transformations of the fields in the NR case, as well as the terms in the four-derivative action depending on the b-field. Interestingly, the corrections to the metric degrees of freedom cannot be fully trivialized, as in the relativistic case, in order to preserve the convergence of the theory. As HSZ theory interpolates order by order between heterotic and bosonic string theories, the results of this work can be interpreted as a truncation of the four-derivative structure of heterotic supergravity in the NR limit.