On Existence of Nontrivial Fixed Points in Large $N$ Gauge Theory in More than Four Dimensions

Inspired by a possible relation between large $N$ gauge theory and string theory, we search for nontrivial fixed points in large $N$ gauge theory in more than four dimensions. We study large $N$ gauge theory through Monte Carlo simulation of the twisted Eguchi-Kawai model in six dimensions as well as in four dimensions. The phase diagram of the system with the two coupling constants which correspond to the standard plaquette action and the adjoint term has been explored.