Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere

TL;DR

This paper uses Monte Carlo simulations to explore the phase structure of a noncommutative U(1) gauge theory on the fuzzy sphere, identifying three distinct phases and their transition points.

Contribution

It provides the first non-perturbative analysis of the phase diagram of NC gauge theory on the fuzzy sphere, including numerical determination of the triple point.

Findings

Identification of three phases: matrix, weak coupling fuzzy sphere, strong coupling fuzzy sphere.

Agreement between numerical results and theoretical predictions for transition lines.

Measurement of the triple point location.

Abstract

We find using Monte Carlo simulation the phase structure of noncommutative U(1) gauge theory in two dimensions with the fuzzy sphere S^2_N as a non-perturbative regulator. There are three phases of the model. i) A matrix phase where the theory is essentially SU(N) Yang-Mills reduced to zero dimension . ii) A weak coupling fuzzy sphere phase with constant specific heat and iii) A strong coupling fuzzy sphere phase with non-constant specific heat. The order parameter distinguishing the matrix phase from the sphere phase is the radius of the fuzzy sphere. The three phases meet at a triple point. We also give the theoretical one-loop and 1/N expansion predictions for the transition lines which are in good agreement with the numerical data. A Monte Carlo measurement of the triple point is also given.