Diffeomorphism invariant SU(N) gauge theories

TL;DR

This paper introduces a class of diffeomorphism invariant SU(N) gauge theories in N^2 dimensions with unique properties, including a specific number of local degrees of freedom and a simplified constraint structure, with some discussion on non-perturbative quantization.

Contribution

It presents a new class of gauge theories with invariant properties and analyzes their degrees of freedom and constraint algebra, including a brief outline of their non-perturbative quantization.

Findings

Theories have (N^2-3)(N^2-1) local degrees of freedom.

The constraint for time reparametrizations is identically satisfied.

A related class in N^2-1 dimensions has the constraint algebra of general relativity.

Abstract

We describe a class of diffeomorphism invariant SU(N) gauge theories in N^2 dimensions, together with some matter couplings. These theories have (N^2-3)(N^2-1) local degrees of freedom, and have the unusual feature that the constraint associated with time reparametrizations is identically satisfied. A related class of SU(N) theories in N^2-1 dimensions has the constraint algebra of general relativity, but has more degrees of freedom. Non-perturbative quantization of the first type of theory via SU(N) spin networks is briefly outlined.