Probing the Holographic Universe: Aspects of Entanglement Entropy Modifications

TL;DR

The thesis addresses how energy fluctuations and acceleration modify entanglement entropy in holographic quantum gravity settings. It combines dS horizon holography with 1-loop corrections to reveal a transition from a flat to an area-law entanglement spectrum while preserving a finite Hilbert space, and extends holographic Renyi entropy to theories with a global $U(1)$ symmetry using non-linear electrodynamics, showing spontaneous symmetry breaking and a reduced leading $\langle TT\rangle$ coefficient. The work also analyzes three-dimensional hairy accelerating black holes, employing Dong’s entropy formula to show that increasing acceleration reduces the accessible boundary region and the entanglement entropy, signaling a loss of information in the dual CFT. Collectively, the results illuminate how quantum fluctuations and acceleration shape entanglement structures and central charges in holographic duals, with implications for the consistency of quantum gravity and the holographic dictionary across dS and AdS regimes.

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.

Figures (14)

• Figure 1: The RT minimal surface extends to the bulk of AdS and is its boundary coincides with the entangling region.
• Figure 2: Difference of the density of free energies of the black hole \ref{['fcataldo']} and thermal AdS for various values of ${\tilde{\mu}}_{\rm E}$ .
• Figure 3: Corrected Renyi entropy as a function of $n$ on the left panel, and $\frac{n}{n-1}\frac{S_n(\mu)}{S_1(0)}$ on the right panel both normalized by the zero-charge limit of the entanglement entropy $S_1(0)$, for different values of the chemical potential with ${\mathtt{V}} = 10^{40}$ . From bottom to top, the curves corresponds to ${\tilde{\mu}} = 0,0.2,0.4,0.6,0.8,1$.
• Figure 4: Corrected Renyi entropy for three-dimensional gravity coupled to Coulomb sources with logarithmic corrections as a function of $n$ normalised by $S_1(0)$ on the left panel, and $\frac{n}{n-1}\frac{S_n(\mu)}{S_1(0)}$ on the right panel, for different values of ${\tilde{\mu}}$ with a UV cutoff so that ${\mathtt{V}} = 1$ . From top to bottom, the curves corresponds to ${\tilde{\mu}} = 0,0.2,0.4,0.6,0.8,1$.
• Figure 5: Corrected charged Renyi entropy for three-dimensional gravity coupled to conformal electrodynamics with a UV cutoff such that ${\mathtt{V}} = 10^{40}$ as a function of the chemical potential normalized by the entanglement entropy of the uncharged limit $S_1(0)$ on the left panel, and normalised by the entanglement entropy $S_1(\mu)$ on the right panel. From top to bottom, the curves corresponds to $n = 1,2,3,4,5$ .