Chaos from massive deformations of Yang-Mills matrix models
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Springer
Received: January 8, Revised: July 12, Accepted: August 30, Published: October 1,
2020 2020 2020 2020
K. Ba¸skan, S. K¨ urk¸cu ¨oˇ glu, O. Oktay and C. Ta¸scı Middle East Technical University, Department of Physics, Dumlupinar Boulevard, 06800, Ankara, Turkey
E-mail: [email protected], [email protected], [email protected], [email protected] 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 = 16 (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. Keywords: M(atrix) Theories, D-branes, Non-Commutative Geometry ArXiv ePrint: 1912.00932
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)003
JHEP10(2020)003
Chaos from massive deformations of Yang-Mills matrix models
Contents 1 Introduction
1
2 Yang-Mills matrix models with double mass deformation 2.1 Ansatz I and the effective action 2.2 Linear stability analysis in the phase space
4 6 9 11 11 12
4 Ans¨ atz II
21
5 Conclusions and outlook
22
A Review of fuzzy spheres A.1 Fuzzy S 2 A.2 Fuzzy S 4
27 27 27
B Poincar´ e sections
29
1
16 18
Introduction
Recently, there has been intense interest in exploring, modeling and understanding the emergence of chaos from matrix models of Yang-Mills(YM) theories [1–12]. Attention has been focused on examining the many aspects and features of chaos in the matrix models of primary interest within the context of M-theory and string theories, namely in the BFSS and BMN models [13–19]. These models are supersymmetric SU(N ) gauge theories in 0 + 1-dimensions, whose bosonic part consist of nine N × N matrices and commonly referred to as matrix quantum mechanics in the literature. BFSS model is associated to the type II-A string theory and appears as the DLCQ of the M-theory in the flat background, while the BMN model, being a deformation of the BFSS involving quadratic and qubic terms preserving the maximal amount of supersymmetry, is the discrete light cone quantization(DLCQ) of M-theory on the pp-wave background. They describe the dynamics of N -coincident D0-branes in flat and spherical backgrounds, respectively; the latter being due to the fact that fuzzy 2-spheres are vacuum configurations in th
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