Hietarinta Chern–Simons supergravity and its asymptotic structure

Patrick Concha; Octavio Fierro; Evelyn Rodríguez

doi:10.1140/epjc/s10052-024-12468-4

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 102
https://doi.org/10.1140/epjc/s10052-024-12468-4

Regular Article - Theoretical Physics

Hietarinta Chern–Simons supergravity and its asymptotic structure

Patrick Concha¹^,2^a, Octavio Fierro³ and Evelyn Rodríguez¹^,2

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, Concepción, Chile
³ Facultad de Ingeniería, Arquitectura y Diseño, Universidad San Sebastián, Lientur 1457, 4080871, Concepción, Chile

^a patrick.concha@ucsc.cl

Received: 3 January 2024
Accepted: 21 January 2024
Published online: 30 January 2024

Abstract

In this paper we present the Hietarinta Chern–Simons supergravity theory in three space-time dimensions which extends the simplest Poincaré supergravity theory. After approaching the construction of the action using the Chern–Simons formalism, the analysis of the corresponding asymptotic symmetry algebra is considered. For this purpose, we first propose a consistent set of asymptotic boundary conditions for the aforementioned supergravity theory whose underlying symmetry corresponds to the supersymmetric extension of the Hietarinta algebra. We then show that the corresponding charge algebra contains the super- ${bms}_{3}$ ${{\mathfrak {bms}}}_{3}$ algebra as subalgebra, and has three independent central charges. We also show that the obtained asymptotic symmetry algebra can alternatively be recovered as a vanishing cosmological constant limit of three copies of the Virasoro algebra, one of which is augmented by supersymmetry.

© The Author(s) 2024

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