| Summary: | 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.
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