Black Holes and Entanglement Entropy

Author: Dadras, Pouria

Year: 2021

Degree: Dissertation (Ph.D.)

Advisor: Kitaev, Alexei

Committee Members: Kapustin, Anton N.; Simmons-Duffin, David; Carroll, Sean M.; Kitaev, Alexei

Option: Physics

DOI: 10.7907/pfnj-m623

Abstract

We study the deformation of the thermofield-double (TFD) under evolution by a double-traced operator by computing its entanglement entropy. After saturation, the entanglement change leads to the temperature change. In Jackiw-Teitelboim gravity, the new temperature can be computed independently from two-point function by considering the Schwarzian modes. We will also derive the entanglement entropy from the Casimir associated with the SL(2,R) symmetry. From AdS/CFT correspondence, where TFD is dual to a two-sided black hole, such deformations correspond to the coherent shrinking or expansion of the black hole.

Next, we compute the entanglement entropy after coupling a system to the bath perturbatively as a function of κ, the system-bath coupling. At very early times where the entanglement entropy is a logarithmic function of time, the leading contribution is due to the terms of order 2s in the coupling where s is the number of replicas. In the middle time, the entanglement goes linear as a function of time. Assuming saturation at a later time, we will study the effect of an external perturbation to the entropy at an early time where it is related to the OTOCs. A major simplification appears when the system saturates the chaos bound.

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