Quantum Aspects of GMS Solutions of Noncommutative Field Theory and Large N Limit of Matrix Models

TL;DR

This paper explores the quantum behavior of GMS solutions in noncommutative field theories at large noncommutativity, revealing their connection to large N matrix models and the effects of quantum fluctuations on their stability.

Contribution

It establishes a quantitative link between GMS solutions and large N matrix models, showing how quantum effects influence their stability and relation to saddle-point solutions.

Findings

GMS solutions are quantum mechanically sensible with appropriate joint scaling of $ heta$ and N.

At large 't Hooft coupling, GMS solutions become destabilized by quantum effects.

GMS solutions are recovered from saddle-point solutions at small 't Hooft coupling.

Abstract

We investigate quantum aspects of Gopakumar-Minwalla-Strominger (GMS) solutions of noncommutative field theory (NCFT) at large noncommutativity limit, $\theta \to \infty$. Building upon a quantitative map between operator formulation of 2-(respectively, (2+1))-dimensional NCFTs and large $N$ matrix models of $c=0$ (respectively, $c=1$) noncritical strings, we show that GMS solutions are quantum mechanically sensible only if we make appropriate joint scaling of $\theta$ and $N$. For 't Hooft's planar scaling, GMS solutions are replaced by large $N$ saddle-point solutions. GMS solutions are recovered from saddle-point solutions at small 't Hooft coupling regime, but are destabilized at large 'tHooft coupling regime by quantum effects. We make comparisons between these large $N$ effects and recently studied infrared effects in NCFTs. We estimate U(N) symmetry breaking gradient effects and argue that they are suppressed only at small 't Hooft coupling regime.