The meaning of infrared singularities in noncommutative gauge theories

We point out that the leading infrared singular terms in the effectiveactions of noncommutative gauge theories arising from nonplanar loop diagramshave a natural interpretation in terms of the matrix model (operator)formulation of these theories. In this formulation (for maximal spatialnoncommutativity), noncommutative space arises as a configuration of aninfinite number of D-particles. We show that the IR singular terms correspondto instantaneous linear potentials between these D-particles resulting from thezero point energies of fluctuations about this background. For theories withfewer fermionic than bosonic degrees of freedom, such as pure noncommutativegauge theory, the potential is attractive and renders the theory unstable. Withmore fermionic than bosonic degrees of freedom, the potential is repulsive andwe argue that the theory is stable, though oddly behaved.Comment: 16 pages, LaTeX, 1 figure, v2: references adde