# Non-Abelian gauge theories invariant under diffeomorphisms

## TL;DR

This paper constructs a class of three-dimensional diffeomorphism and gauge invariant theories, exploring their degrees of freedom based on gauge group dimension and constraints, including special cases like Chern-Simons.

## Contribution

It introduces a canonical framework for building diffeomorphism and gauge invariant theories in three dimensions, including models without existing action descriptions.

## Key findings

- Theories' local degrees of freedom depend on gauge group and constraints.
- Identified special cases with maximal and zero degrees of freedom.
- Included a formulation of Chern-Simons theory as a special case.

## Abstract

We discuss diffeomorphism and gauge invariant theories in three dimensions motivated by the fact that some models of interest do not have a suitable action description yet. The construction is based on a canonical representation of symmetry generators and on building of the corresponding canonical action. We obtain a class of theories whose number of local degrees of freedom depends on the dimension of the gauge group and the number of the independent constraints. By choosing the latter, we focus on three special cases, starting with a theory with maximal local number of degrees of freedom and finishing with a theory with zero degrees of freedom (Chern-Simons).