A Topological Model for Two Dimensional Gravity Coupled to Matter

TL;DR

This paper develops a topological gauge theory-based model for two-dimensional gravity coupled with matter, exploring its equations of motion, quantum aspects, and topological invariants.

Contribution

It introduces a novel topological model for 2D gravity with matter coupling based on specific gauge groups, extending previous models.

Findings

Derived equations of motion incorporating matter

Analyzed the quantum theory of the model

Presented explicit formulas for topological invariants

Abstract

Starting from a topological gauge theory in two dimensions with symmetry groups $ISO(2,1)$, $SO(2,1)$ and $SO(1,2)$ we construct a model for gravity with non-trivial coupling to matter. We discuss the equations of motion which are connected to those of previous related models but incorporate matter content. We also discuss the resulting quantum theory and finally present explicit formul\ae $\;$ for topological invariants.