Thermodynamics of Fuzzy Spheres in PP-wave Matrix Model

TL;DR

This paper analyzes the thermodynamic stability of fuzzy spheres in a pp-wave matrix model, showing a temperature-dependent phase transition where fuzzy spheres become more stable than trivial vacua.

Contribution

It provides an exact free energy calculation for fuzzy spheres in the large  limit and demonstrates a temperature-driven phase transition in the model.

Findings

Fuzzy sphere vacuum becomes more stable than trivial vacuum at high temperature

Exact free energy computed in the  limit for arbitrary N

Supports condensation of fluctuations into fuzzy spheres above a critical temperature

Abstract

We discuss thermodynamics of fuzzy spheres in a matrix model on a pp-wave background. The exact free energy in the fuzzy sphere vacuum is computed in the \mu -> \infty limit for an arbitrary matrix size N. The trivial vacuum dominates the fuzzy sphere vacuum at low temperature while the fuzzy sphere vacuum is more stable than the trivial vacuum at sufficiently high temperature. Our result supports that the fluctuations around the trivial vacuum would condense to form an irreducible fuzzy sphere above a certain temperature.