Dynamical tachyons on fuzzy spheres

TL;DR

This paper analyzes the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the BMN matrix model, revealing classical tachyons at intersection angles and relating them to Yang-Mills instabilities, with implications for system thermalization.

Contribution

It provides an analytical computation of tachyonic modes in fuzzy sphere configurations and explores their dynamics and potential role in thermalization within the BMN matrix model.

Findings

Classical tachyons develop at intersecting fuzzy spheres.

Spectrum of modes can be computed analytically.

Tachyonic modes may influence thermalization processes.

Abstract

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the BMN plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.