$D=4$ topological gravity from gauging the Maxwell-special-affine group

TL;DR

This paper develops a gauge theory of a Maxwell-extended special-affine algebra leading to a four-dimensional topological gravity model, with new algebraic structures and insights into Bianchi identities.

Contribution

It introduces a novel Maxwell extension of the special-affine algebra and constructs a corresponding gauge theory for four-dimensional topological gravity.

Findings

Derived the Maxwell extension of the special-affine algebra.

Constructed the gauge theory and topological gravity action.

Connected Bianchi identities with equations of motion solutions.

Abstract

In this paper, the Maxwell extension of the special-affine algebra is obtained and corresponding non-linear realization is constructed. We give also the differential realization of the generators of the extended symmetry. Moreover, we present the gauge theory of the Maxwell special-affine algebra and the topological gravity action in four dimensions. As a conclusion, we show that the Bianchi identities can be found by using the solution of the equations of motion.