Chaos from massive deformations of Yang-Mills matrix models

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) × SO(3) × ℤ2. 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 6 (n + 1)(n + 2)(n + 3), for n = 1, 2, · · · , 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 2πT , and below which it will eventually be violated.

Entanglement dynamics of coupled oscillators from Gaussian states

“…Although calculating entanglement entropy in ordinary field theories is a rather difficult task, the numerical computations of the entanglement entropy in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model were recently performed in reference [16] by using the covariance matrix representations of Gaussian states. In this regard, a valuable direction of research would be to investigate the time-dependence of the entanglement entropy in a Yang-Mills matrix model with two distinct mass deformation terms, whose emerging chaotic motions and dynamics of thermalization have been recently studied in a series of papers [26,27]. Aside from the mass deformation terms keeping the gauge invariance intact, this model contains the same matrix content as the bosonic part of the BFSS matrix model and provides an ideal system for the use of Gaussian state approximation.…”

Thermalization in massive deformations of Yang-Mills matrix models

“…The BFSS matrix model is a Yang-Mills theory in 0 + 1 dimensions which arises from the dimensional reduction of the Yang-Mills theory in 9 + 1 dimensions with N = 1 supersymmetry [5]. In this paper, we focus upon a gauge invariant double mass deformation of the bosonic part of the BFSS action which may be specified as [16]…”

“…) ‡ We refer the interested reader to [16][17][18] for similar applications of this method in matrix models. We may also consider the effects of adding random fluctuation terms to the matrix model.…”

“…In this paper, our main interest is to analyze the dynamics of thermalization in a Yang-Mills matrix model with two distinct mass deformation terms, whose emerging chaotic motions have been investigated in [16]. This model has the same matrix content as the bosonic part of the BFSS matrix model, but also contains mass deformation terms that keep the gauge invariance intact.…”

Chaotic Dynamics of the Mass Deformed ABJM Model

“…Studies on exploring the structure of chaotic dynamics emerging from the matrix quantum mechanics has been continuing with growing interest for quite sometime [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Early investigations on the chaotic dynamics of Yang-Mills (YM) gauge theories dates back to 80s [15][16][17] and in the context of the Banks-Fischler-Shenker-Susskind (BFSS) model [18] to the work Arefeva et.…”