Probing the Holographic Universe: Aspects of Entanglement Entropy Modifications

TL;DR

This paper explores how energy fluctuations, acceleration, and symmetries influence entanglement entropy in holographic theories, revealing modifications to the entropy area law and information loss mechanisms.

Contribution

It introduces 1-loop corrections to entanglement entropy calculations, extends holographic frameworks to charged theories, and analyzes the impact of acceleration on information accessibility.

Findings

1-loop corrections disrupt flat entanglement spectrum

Spontaneous symmetry breaking reduces $\

Acceleration decreases boundary region and entanglement entropy

Abstract

Entanglement entropy is crucial for understanding the link between quantum mechanics and information theory. This thesis investigates how energy fluctuations and acceleration affect entanglement entropy through three key scenarios. First, we analyze entanglement between disjoint Rindler observers in de Sitter spacetime. We introduce 1-loop corrections to the partition function of the conformal field theory, disrupting the previously flat entanglement spectrum and resulting in an area law for entanglement entropy, while preserving the finiteness of the Hilbert space. Next, we extend the holographic entanglement entropy framework to field theories with global $U(1)$ symmetry, considering non-linearly charged theories and their thermal and quantum fluctuations. We find that the dual theory experiences spontaneous symmetry breaking and a reduction in the leading-order coefficient of the $\langle TT\rangle$ correlator due to quantum corrections. Using conformal electrodynamics coupled with three-dimensional gravity as an example, we explore a black hole solution and its connection to two-dimensional free bosons. Finally, we investigate three-dimensional accelerating black holes, revealing that increased acceleration reduces the accessible boundary region and, consequently, the entanglement entropy. This suggests a loss of information in the dual theory due to acceleration.