Chaos exponents of SYK traversable wormholes
- URL: http://arxiv.org/abs/2009.10759v1
- Date: Tue, 22 Sep 2020 18:41:34 GMT
- Title: Chaos exponents of SYK traversable wormholes
- Authors: Tomoki Nosaka and Tokiro Numasawa
- Abstract summary: We study the chaos exponent, the exponential growth rate of the out-of-time-ordered four point functions, in a two coupled SYK models.
We see that as the temperature decreases the chaos exponent exhibits a discontinuous fall-off from the value of order the universal bound $2pi/beta$ at the critical temperature of the phase transition.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper we study the chaos exponent, the exponential growth rate of the
out-of-time-ordered four point functions, in a two coupled SYK models which
exhibits a first order phase transition between the high temperature black hole
phase and the low temperature gapped phase interpreted as a traversable
wormhole. We see that as the temperature decreases the chaos exponent exhibits
a discontinuous fall-off from the value of order the universal bound
$2\pi/\beta$ at the critical temperature of the phase transition, which is
consistent with the expected relation between black holes and strong chaos.
Interestingly, the chaos exponent is small but non-zero even in the wormhole
phase. This is surprising but consistent with the observation on the decay rate
of the two point function [arXiv:2003.03916], and we found the chaos exponent
and the decay rate indeed obey the same temperature dependence in this regime.
We also studied the chaos exponent of a closely related model with single SYK
term, and found that the chaos exponent of this model is always greater than
that of the two coupled model in the entire parameter space.
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