  We study the quantum mechanical model obtained as a dimensional reduction of
N=1 super Yang-Mills theory to a periodic light-cone "time". After mapping the
theory to a cohomological field theory, the partition function (with periodic
boundary conditions) regularized by a massive term appears to be equal to the
partition function of the twisted matrix oscillator. We show that this
partition function perturbed by the operator of the holonomy around 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.
