The non-relativistic limit of HSZ Theory

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.

💡 Research Summary

The paper investigates the non‑relativistic (NR) limit of the Hohm‑Siegel‑Zwiebach (HSZ) theory, a higher‑derivative gravity model that is exactly and manifestly invariant under T‑duality. HSZ theory is formulated on a doubled space with an O(D,D) invariant metric η_{MN}, a symmetric double metric M_{MN}, and a generalized dilaton d. The strong constraint ∂^M∂M·=0 is imposed, ensuring closure of the deformed gauge algebra. The action is written compactly as S=∫d^{2D}X e^{-2d}⟨M|M⟩⋆, where the inner product and the star product encode all higher‑derivative corrections. At the two‑derivative level the theory reduces to ordinary Double Field Theory (DFT); at four and six derivatives it contains non‑trivial deformations that are still T‑duality covariant.

To explore the NR regime, the authors introduce a large parameter c (c→∞) and expand the usual spacetime fields as
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