Non Abelian BF theories with sources and 2-D gravity

TL;DR

This paper explores non-Abelian BF theories with point sources on 2D manifolds, providing general solutions and connecting to 2D gravity models using the extended Poincaré group.

Contribution

It presents the most general solutions for non-Abelian BF theories with sources on various 2D manifolds and links these to 2D gravity models via the extended Poincaré group.

Findings

Derived general solutions for field equations on different 2D manifolds.

Connected non-Abelian BF theories to 2D gravity models.

Analyzed the role of the extended Poincaré group in this context.

Abstract

We study the interaction of non-Abelian topological $BF$ theories defined on two dimensional manifolds with point sources carrying non-Abelian charges. We identify the most general solution for the field equations on simply and multiply connected two-manifolds. Taking the particular choice of the so-called extended Poincar\'e group as the gauge group we discuss how recent discussions of two dimensional gravity models do fit in this formalism.