Noncommutative gauge theories on $\mathbb{R}^2_\theta$ as matrix models

TL;DR

This paper investigates noncommutative gauge theories on 2D Moyal space using matrix model techniques, revealing properties of propagators, correlations, and vacuum stability in specific symmetric vacua.

Contribution

It introduces a matrix model approach to noncommutative gauge theories on 54 space, analyzing propagators and vacuum stability for particular symmetric vacua.

Findings

Propagators can be expressed with Chebyshev polynomials.

Non-vanishing correlations exist at large distances.

Only certain symmetric vacua lead to rapidly decaying propagators.

Abstract

We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with polynomial interaction terms. For a particular vacuum, we can invert the kinetic operator which is related to a Jacobi operator. The resulting propagator can be expressed in terms of Chebyschev polynomials of second kind. We show that non vanishing correlations exist at large separations. General considerations on the kinetic operators stemming from the other class of symmetric vacua, indicates that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed.