Five dimensional Chern-Simons Gravity for the expanded (anti)-de Sitter gauge group C$_5$

TL;DR

This paper explores the Hamiltonian structure of a five-dimensional Chern-Simons gravity theory based on an expanded (anti-)de Sitter gauge algebra, revealing new symmetries and the presence of curvature-squared terms.

Contribution

It introduces a novel 5D Chern-Simons gravity model with an expanded gauge algebra, identifying new symmetries and analyzing its degrees of freedom.

Findings

Presence of curvature-squared terms in the action.

Introduction of 'crossed diffeomorphisms' symmetry.

The theory is 'generic' with dependent constraints.

Abstract

We study the Hamiltonian dynamics of a five-dimensional Chern-Simons theory for the gauge algebra $C_5$ of Izaurieta, Rodriguez and Salgado, the so-called S$_H$-expansion of the 5D (anti-)de Sitter algebra (a)ds, based on the cyclic group $\mathbb{Z}_4$. The theory consists of a 1-form field containing the (a)ds gravitation variables and 1-form field transforming in the adjoint representation of (a)ds. The gravitational part of the action necessarily contains a term quadratic in the curvature, beyond the Einstein-Hilbert and cosmological terms, for any choice of the two independent coupling constants. The total action is also invariant under a new local symmetry, called "crossed diffeomorphisms", beyond the usual space-time diffeomorphisms. The number of physical degrees of freedom is computed. The theory is shown to be "generic" in the sense of Ba\~nados, Garay and Henneaux, i.e., the constraint associated to the time diffeomorphisms is not independent from the other constraints.