Scalar and tensorial topological matter coupled to (2+1)-dimensional gravity:A.Classical theory and global charges

TL;DR

This paper explores a (2+1)-dimensional gravity model coupled with scalar and tensorial topological matter, analyzing its classical solutions, global charges, and reformulation as a generalized Chern-Simons theory.

Contribution

It provides a canonical analysis of the coupled model, identifies its solutions, and demonstrates its algebraic structure and reformulation as a higher gauge theory.

Findings

Existence of BTZ-like black hole solutions

Presence of homogeneous and inhomogeneous FRW cosmologies

Global charge algebra extends Kac-Moody and Virasoro structures

Abstract

We consider the coupling of scalar topological matter to (2+1)-dimensional gravity. The matter fields consist of a 0-form scalar field and a 2-form tensor field. We carry out a canonical analysis of the classical theory, investigating its sectors and solutions. We show that the model admits both BTZ-like black-hole solutions and homogeneous/inhomogeneous FRW cosmological solutions.We also investigate the global charges associated with the model and show that the algebra of charges is the extension of the Kac-Moody algebra for the field-rigid gauge charges, and the Virasoro algebrafor the diffeomorphism charges. Finally, we show that the model can be written as a generalized Chern-Simons theory, opening the perspective for its formulation as a generalized higher gauge theory.