The Meaning of Infrared Singularities in Noncommutative Gauge Theories

TL;DR

This paper interprets infrared singularities in noncommutative gauge theories as linear potentials between D-particles in a matrix model, revealing stability conditions based on fermionic and bosonic degrees of freedom.

Contribution

It provides a novel interpretation of IR singularities in noncommutative gauge theories through the matrix model framework, linking them to D-particle interactions.

Findings

IR singularities correspond to linear potentials between D-particles

Pure gauge theories with fewer fermions are unstable due to attractive potentials

Theories with more fermions are stable but exhibit unusual behavior

Abstract

We point out that the leading infrared singular terms in the effective actions of noncommutative gauge theories arising from nonplanar loop diagrams have a natural interpretation in terms of the matrix model (operator) formulation of these theories. In this formulation (for maximal spatial noncommutativity), noncommutative space arises as a configuration of an infinite number of D-particles. We show that the IR singular terms correspond to instantaneous linear potentials between these D-particles resulting from the zero point energies of fluctuations about this background. For theories with fewer fermionic than bosonic degrees of freedom, such as pure noncommutative gauge theory, the potential is attractive and renders the theory unstable. With more fermionic than bosonic degrees of freedom, the potential is repulsive and we argue that the theory is stable, though oddly behaved.