Lattice study of the simplified model of M-theory for larger gauge groups

TL;DR

This study uses lattice simulations to explore the behavior of supersymmetric Yang-Mills quantum mechanics with larger gauge groups, providing insights into phase transitions potentially related to M-theory black hole and excitation phases.

Contribution

It extends lattice analysis of supersymmetric quantum mechanics to larger gauge groups (N=3 to 8) and introduces a new noncompact lattice formulation.

Findings

Different behaviors observed at low and high temperatures.

Transition temperature scales with N consistent with 't Hooft scaling.

Results suggest a possible phase transition or crossover in the system.

Abstract

Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is dis cussed. First results of the quenched Monte Carlo simulations, for D=4 and with higher g auge groups (3 <= N <= 8), are presented. We confirm an earlier (N=2) evidence tha t the system reveals different behaviours at low and high temperatures separated by a narrow transiti on region. These two regimes may correspond to a black hole and elementary excitations phases conjectured in the M-theory. Dependence 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.