Thermodynamic Behavior of Fuzzy Membranes in PP-Wave Matrix Model

TL;DR

This paper investigates the thermodynamic interactions of fuzzy membranes in a pp-wave matrix model at finite temperature, revealing an attractive potential and supersymmetry breaking effects.

Contribution

It provides a detailed analysis of the thermodynamic behavior of fuzzy membranes, including numerical and analytical results on their interactions at finite temperature.

Findings

Attractive potential causes fuzzy spheres to fall into the origin

Supersymmetry is broken at finite temperature

Free energy approximated by a polylogarithm function

Abstract

We discuss a two-body interaction of membrane fuzzy spheres in a pp-wave matrix model at finite temperature by considering a fuzzy sphere rotates with a constant radius r around the other one sitting at the origin in the SO(6) symmetric space. This system of two fuzzy spheres is supersymmetric at zero temperature and there is no interaction between them. Once the system is coupled to the heat bath, supersymmetries are completely broken and non-trivial interaction appears. We numerically show that the potential between fuzzy spheres is attractive and so the rotating fuzzy sphere tends to fall into the origin. The analytic formula of the free energy is also evaluated in the large N limit. It is well approximated by a polylog-function.