Non supersymmetric large N background for two Yang-Mills coupled matrices

Abstract

The study of matrix models is of considerable significance. In this thesis we study the large N quantum mechanics of two matrices (X1,X2), coupled via a Yang-Mills interaction, in a non supersymmetric setting. Of the two matrices, X1 is treated exactly,while X2 is understood as an “impurity” in the background of the first. Considering the ground statewavefunctionwith no X2 “impurities”, it is observed that this state depends on the eigenvalues of the X1 matrix, resulting in additional shifts in the calculation of the kinetic term for the X1 sector. This results in an effective potential which, using the results of collective field theory, is used to obtain the planar large N nonsupersymmetric background. The system is studied in both weak and strong coupling. The strong coupling system is free of infrared divergences.