Higher Gauge Theory and Gravity in (2+1) Dimensions

TL;DR

This paper explores applying higher gauge theory to (2+1)-dimensional gravity, demonstrating a model that encompasses various geometries and opens new avenues for understanding gravity with matter in this framework.

Contribution

It formulates a (2+1)-dimensional gravity model as a higher gauge theory, extending the application of higher gauge concepts to gravitational systems with matter.

Findings

The $oldsymbol{ extSigmaoldPhi EA}$ model admits black-hole, particle-like, and cosmological solutions.

The model can be described both as a standard gauge theory and as a higher gauge theory.

This approach provides a new framework for studying gravity coupled to matter in (2+1) dimensions.

Abstract

Non-abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher dimensional (2-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-abelian generalizations of the Yang-Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in (2+1) dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields - the $\Sigma\Phi EA$ model - can be formulated both as a standard gauge theory and as a higher gauge theory. Since the model has a very rich structure - it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson-Friedman-Walker cosmological-like expanding geometries - this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in (2+1) dimensions coupled to matter in an entirely new framework.