Three-dimensional non-relativistic Hietarinta supergravity

Patrick Concha; Evelyn Rodríguez; Sebastián Salgado

doi:10.1140/epjc/s10052-025-13761-6

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 47
https://doi.org/10.1140/epjc/s10052-025-13761-6

Regular Article - Theoretical Physics

Three-dimensional non-relativistic Hietarinta supergravity

Patrick Concha¹^,2^a, Evelyn Rodríguez¹^,2 and Sebastián Salgado³

¹ Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Alonso de Ribera, 2850, Concepción, Chile
² Grupo de Investigación en Física Teórica, GIFT, Universidad Católica de la Santísima Concepción, Alonso de Ribera, 2850, Concepción, Chile
³ Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile

^a patrick.concha@ucsc.cl

Received: 9 September 2024
Accepted: 28 December 2024
Published online: 21 January 2025

Abstract

In this work we present the non-relativistic regime of the Hietarinta gravity theory and its extension to supergravity. At the bosonic level, we derive the non-relativistic version of the Hietarinta model by employing a contraction process and addressing the non-degeneracy of the invariant metric. To incorporate supersymmetry, we apply the Lie algebra expansion method to obtain the non-relativistic formulation of $N = 2$ ${\mathcal {N}}=2$ Hietarinta supergravity. Our results reveal that the non-relativistic Hietarinta theory encompasses the extended Bargmann (super)gravity as a special case, yet it differs significantly from other existing non-relativistic (super)gravity models. Furthermore, we generalize our analysis to include a cosmological constant term in the non-relativistic Hietarinta (super)gravity action and examine its effects on the torsion structure.

© The Author(s) 2025

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