Abstract
This note is devoted to the investigation of Susskind’s proposal [1] concerning the correspondence between the operator growth in chaotic theories and the radial momenta of the particle falling in the AdS black hole. We study this proposal and consider the simple example of an operator with the global charge described by the charged particle falling to the Reissner-Nordstrom-AdS black hole. Different charges of the particle lead to qualitatively different behavior of the particle momenta and consequently change of the operator size behavior. This holographic result is supported by different examples of chaotic models with a finite chemical potential where the suppression of chaos has been observed.
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References
L. Susskind, Why do things fall?, arXiv:1802.01198 [INSPIRE].
A.R. Brown, H. Gharibyan, A. Streicher, L. Susskind, L. Thorlacius and Y. Zhao, Falling toward charged black holes, Phys. Rev. D 98 (2018) 126016 [arXiv:1804.04156] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
D.A. Roberts, D. Stanford and A. Streicher, Operator growth in the SYK model, JHEP 06 (2018) 122 [arXiv:1802.02633] [INSPIRE].
R. Bhattacharya, S. Chakrabarti, D.P. Jatkar and A. Kundu, SYK model, chaos and conserved charge, JHEP 11 (2017) 180 [arXiv:1709.07613] [INSPIRE].
T. Azeyanagi, F. Ferrari and F.I. Schaposnik Massolo, Phase diagram of planar matrix quantum mechanics, tensor and Sachdev-Ye-Kitaev models, Phys. Rev. Lett. 120 (2018) 061602 [arXiv:1707.03431] [INSPIRE].
T. Rakovszky, F. Pollmann and C.W. von Keyserlingk, Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation, Phys. Rev. X 8 (2018) 031058 [arXiv:1710.09827] [INSPIRE].
V. Khemani, A. Vishwanath and D.A. Huse, Operator spreading and the emergence of dissipation in unitary dynamics with conservation laws, Phys. Rev. X 8 (2018) 031057 [arXiv:1710.09835] [INSPIRE].
S. Pai, M. Pretko and R.M. Nandkishore, Localization in fractonic random circuits, arXiv:1807.09776 [INSPIRE].
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ArXiv ePrint: 1806.05574
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Ageev, D.S., Aref’eva, I.Y. When things stop falling, chaos is suppressed. J. High Energ. Phys. 2019, 100 (2019). https://doi.org/10.1007/JHEP01(2019)100
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DOI: https://doi.org/10.1007/JHEP01(2019)100