Chaos from Massive Deformations of Yang-Mills Matrix Models

TL;DR

This paper investigates chaotic dynamics in a mass-deformed SU(N) Yang-Mills matrix model, analyzing Lyapunov exponents to understand temperature bounds related to the MSS chaos bound.

Contribution

It introduces a specific ansatz with fuzzy spheres to study chaos in a deformed matrix model and numerically computes Lyapunov spectra across different energies and matrix sizes.

Findings

Largest Lyapunov exponents depend on energy and matrix size.

Results suggest bounds on temperature for chaos saturation and violation.

Model provides insights into chaos bounds in gauge theories.

Abstract

We focus on an $SU(N)$ Yang-Mills gauge theory in $0+1$-dimensions with the same matrix content as the bosonic part of the BFSS matrix model, but with mass deformation terms breaking the global $SO(9)$ symmetry of the latter to $SO(5) \times SO(3) \times {\mathbb Z}_2$. Introducing an ansatz configuration involving fuzzy four and two spheres with collective time dependence, we examine the chaotic dynamics in a family of effective Lagrangians obtained by tracing over the aforementioned ansatz configurations at the matrix levels $N = \frac{1}{6}(n+1)(n+2)(n+3)$, for $n=1,2,\cdots\,,7$. Through numerical work, we determine the Lyapunov spectrum and analyze how the largest Lyapunov exponents(LLE) change as a function of the energy, and discuss how our results can be used to model the temperature dependence of the LLEs and put upper bounds on the temperature above which LLE values comply with the Maldacena-Shenker-Stanford (MSS) bound $2 \pi T $ , and below which it will eventually be violated.