Controlling divergences in the NR limit of the Metsaev–Tseytlin Lagrangian

Determine a covariant method to control all higher-derivative divergences that arise in the non-relativistic limit of the full Metsaev–Tseytlin four-derivative bosonic string supergravity Lagrangian.

Background

The paper develops a diffeomorphism-covariant Newton–Cartan framework with non-metricities to rewrite relativistic curvature invariants in a non-relativistic limit. Within this setup, the authors analyze finite four-derivative contributions originating from the Metsaev–Tseytlin Lagrangian, which encodes part of the bosonic string’s alpha'-level corrections.

Despite presenting many finite terms, the authors explicitly state that they cannot yet control all higher-derivative divergences that appear in the non-relativistic limit of the full Metsaev–Tseytlin Lagrangian, identifying this as an open problem.

References

At the present moment we cannot control all the divergences of the full Metsaev-Tseytlin Lagrangian and for that reason we are not giving an exhaustive analysis of the four-derivative contributions of this Lagrangian in its NR limit. However, the covariant framework developed in this work could be very useful for attacking this open problem.

— Curvatures and Non-metricities in the Non-Relativistic Limit of Bosonic Supergravity  (2601.03342 - Lescano, 6 Jan 2026) in Applications, Subsection "Non-relativistic bosonic alpha'-corrections"