Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature

TL;DR

This study uses Monte Carlo methods to explore the thermodynamics of one-dimensional supersymmetric gauge theories with 4 and 8 supercharges, revealing an exponential decay in internal energy at low temperatures, unlike the 16 supercharge case.

Contribution

First nonperturbative Monte Carlo analysis of 4 and 8 supercharge models showing exponential energy decay, highlighting differences from the 16 supercharge case.

Findings

Internal energy decreases exponentially at low temperature.

Supports the conjecture that zero-energy bound states are absent.

Reveals qualitative differences from 16 supercharge models.

Abstract

We investigate thermodynamic properties of one-dimensional U(N) supersymmetric gauge theories with 4 and 8 supercharges in the planar large-N limit by Monte Carlo calculations. Unlike the 16 supercharge case, the threshold bound state with zero energy is widely believed not to exist in these models. This led A.V. Smilga to conjecture that the internal energy decreases exponentially at low temperature instead of decreasing with a power law. In the 16 supercharge case, the latter behavior was predicted from the dual black 0-brane geometry and confirmed recently by Monte Carlo calculations. Our results for the models with 4 and 8 supercharges indeed support the exponential behavior, revealing a qualitative difference from the 16 supercharge case.