Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II

TL;DR

This paper investigates phase transitions in supersymmetric Yang-Mills matrix models, revealing a transition from a fuzzy sphere geometry to a phase with commuting matrices, and explores the effects of supersymmetry on this transition.

Contribution

It provides a detailed Monte Carlo analysis of phase transitions in D=4 supersymmetric Yang-Mills matrix models with SO(3) mass terms, highlighting the role of supersymmetry in stabilizing the fuzzy sphere.

Findings

Existence of a first/second order transition in bosonic models.

Fuzzy sphere stability in supersymmetric models due to slow crossover.

Eigenvalue distribution follows a non-polynomial law from uniform joint distribution.

Abstract

We present a study of D=4 supersymmetric Yang-Mills matrix models with SO(3) mass terms based on the Monte Carlo method. In the bosonic models we show the existence of an exotic first/second order transition from a phase with a well defined background geometry (the fuzzy sphere) to a phase with commuting matrices with no geometry in the sense of Connes. At the transition point the sphere expands abruptly to infinite size then it evaporates as we increase the temperature (the gauge coupling constant). The transition looks first order due to the discontinuity in the action whereas it looks second order due to the divergent peak in the specific heat. The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition. The transition point is found to scale to zero with N. We conjecture that the transition from the background sphere to the phase of commuting matrices is associated with spontaneous supersymmetry breaking. The eigenvalues distribution of any of the bosonic matrices in the matrix phase is found to be given by a non-polynomial law obtained from the fact that the joint probability distribution of the four matrices is uniform inside a solid ball with radius R. The eigenvalues of the gauge field on the background geometry are also found to be distributed according to this non-polynomial law.