LATTICE STUDY OF THE SIMPLIFIED MODEL OF M-THEORY FOR LARGER GAUGE GROUPS

摘要

Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is discussed. First results of the quenched Monte Carlo simulations, for D=4 and with higher gauge groups ( 3 ≤ N ≤ 8 ), are presented. We confirm an earlier (N=2) evidence that the system reveals different behaviours at low and high temperatures separated by a narrow transition region. These two regimes may correspond to a black hole and elementary excitations phases conjectured in the M-theory. Depen-dence of the "transition temperature" on N is consistent with 't Hooft scaling and shows a smooth saturation of lattice results towards the large N limit. Is not yet resolved if the observed change between the two regimes corresponds to a genuine phase transition or to a gentle crossover. A new, noncompact formulation of the lattice model is also proposed and its advantages are briefly discussed.