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Title: Semiclassical geometry in double-scaled SYK
A<sc>bstract</sc> We argue that at finite energies, double-scaled SYK has a semiclassical approximation controlled by a couplingλin which all observables are governed by a non-trivial saddle point. The Liouville description of double-scaled SYK suggests that the correlation functions define a geometry in a two-dimensional bulk, with the 2-point function describing the metric. For small coupling, the fluctuations are highly suppressed, and the bulk describes a rigid (A)dS spacetime. As the coupling increases, the fluctuations become stronger. We study the correction to the curvature of the bulk geometry induced by these fluctuations. We find that as we go deeper into the bulk the curvature increases and that the theory eventually becomes strongly coupled. In general, the curvature is related to energy fluctuations in light operators. We also compute the entanglement entropy of partially entangled thermal states in the semiclassical limit.  more » « less
Award ID(s):
2209997
PAR ID:
10522242
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2023
Issue:
11
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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