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. Wadia11 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 )
Abstract
We investigate quantum aspects of
Gopakumar-Minwalla-Strominger (GMS) solutions of non-commutative
field
theory (NCFT) in the large non-commutativity limit,
. 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
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
