Dimensionally reduced SYM4 as solvable matrix quantum mechanics

We study the quantum mechanical model obtained as a dimensional reduction o f N = 1 super Yang-Mills theory to a periodic light cone "time''. After map ping the theory to a cohomological field theory, the partition function (wi th periodic boundary conditions) regularized by a massive term appears to b e equal to the partition function of the twisted matrix oscillator. We show that this partition function perturbed by the operator of the holonomy aro und the time circle is a tau function of Toda hierarchy. We solve the model in the large N limit and study the universal properties of the solution in the scaling limit of vanishing perturbation. We find in this limit a phase transition of Gross-Witten type. (C) 2000 Elsevier Science B.V, All rights reserved.