Continuum Limits of “INDUCED QCD”:. Lessons of the Gaussian Model at d=1 and Beyond
Abstract
We analyze the scalar field sector of the KazakovMigdal model of induced QCD. We present a detailed description of the simplest onedimensional (d=1) model which supports the hypothesis of wide applicability of the meanfield approximation for the scalar fields and the existence of critical behavior in the model when the scalar action is Gaussian. Despite the occurrence of various nontrivial types of critical behavior in the d=1 model as N→∞, only the conventional large N limit is relevant for its continuum limit. We also give a meanfield analysis of the N=2 model in any d and show that a saddle point always exists in the region m^{2} > m_{} crit^{2} (= d). In d=1 it exhibits critical behavior as m^{2} > m_{} crit^{2}. However when d>1 there is no critical behavior unless nonGaussian terms are added to the scalar field action. We argue that similar behavior should occur for any finite N thus providing a simple explanation of a recent result of D. Gross. We show that critical behavior at d>1 and m^{2} > m_{} crit^{2} can be obtained by adding a logarithmic term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov—Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behavior of the Gaussian model.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 1993
 DOI:
 10.1142/S0217751X9300059X
 arXiv:
 arXiv:hepth/9208054
 Bibcode:
 1993IJMPA...8.1411K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 31 pages