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Particles and Fields

Eur. Phys. J. C 24, 495-514 (2002)
DOI: 10.1007/s100520200939

Quantum aspects of GMS solutions of non-commutative field theory and large N limit of matrix models

G. Mandal1, S.-J. Rey2 and S.R. Wadia1

1  Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
2  School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea

(Received: 2 January 2002 / Published online: 26 April 2002 - © Springer-Verlag / Società Italiana di Fisica 2002 )

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

© Società Italiana di Fisica, Springer-Verlag 2002