Quantum corrections to holographic entanglement entropy (1307.2892v2)

Abstract: We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.

• The paper introduces one-loop quantum corrections to the classical RT formula by quantifying bulk entanglement across the minimal surface.
• It employs the replica trick alongside rigorous consistency checks, including UV counterterms and Wald-like entropy extensions, to validate the quantum contributions.
• The findings advance our understanding of holographic entanglement entropy, with implications for confining models and thermal regimes in gravitational duals.

Overview of Quantum Corrections to Holographic Entanglement Entropy

The examined research paper primarily addresses the subject of quantum corrections to the holographic calculation of entanglement entropy in quantum field theories that possess a gravitational dual. The Ryu-Takayanagi (RT) prescription serves as the foundation for this work, where the leading order for entanglement entropy computation is derived from the area of a minimal surface in the gravity dual. This paper progresses the understanding by incorporating quantum corrections—specifically at the one loop level—to the RT formula, enhancing the applicability of these computations to the quantum regime.

Holographic Entanglement Entropy and Quantum Considerations

The focal point of the analysis is the entanglement entropy calculation for a boundary region within AdS/CFT. Using the RT prescription, the entanglement entropy at leading order corresponds to the area of a minimal surface in the bulk geometry adhering to the boundary condition of the region on the conformal boundary. Formulated as $$S_{cl}(A) = \frac{{\text{Area}_{\text{min}}}}{4G_N}$$, this classical approximation is central to the paper's exploration of the departures introduced by quantum effects.

The authors introduce an insightful one loop quantum correction to this area-based entanglement computation. The minimal surface divides the bulk into two separate regions, allowing the bulk entanglement entropy between these two regions to serve as the one loop correction's basis. In essence, the bulk quantum fields across these divisions contribute an additional entropic term, expressed as $S_q(A) = S_{\rm bulk-ent}(A_b)$, and other finite corrections cancel the divergencies of the bulk entanglement entropy. These corrections signify the computations departing from classical bulks towards the realms where quantum fields are active.

Theoretical Implications and Methodology

Through thorough theoretical development, the authors deploy the replica trick in static conditions to calculate related Renyi entropies and subsequently entanglement entropy. This methodology allows the authors to delve into the intricate details of quantum corrections as emergent effects from geometric configurations and quantum matter fields in the bulk. Consequently, the quantum correction represents the entanglement across the minimal surface cut, providing a new dimension to understanding through a blend of geometric and quantum field theoretic aspects.

To validate their proposed methodology, the work lays down consistency checks leveraging background geometry changes, Wald-like entropy extensions for higher curvature actions, and stress-energy tensor expectations in quantum fields. Issues such as counterterms required for UV finiteness, and their implications, are elaborated to convey the quantum contributions' full landscape.

Practical Implications and Future Developments

From the research paper, several implications and forward-thinking applications arise. Quantum corrections influence holographic entanglement entropy in scenarios like confining holographic models and thermal bulk states. Particularly, the thermal field in the bulk environment demonstrates volume-proportional entanglement, expounding on how energy distributions interact with entanglement geometries.

Significantly, quantum entanglement reveals non-zero mutual information even for well-separated regions within certain configurations, introducing a nuanced understanding of correlation scopes across boundaries. This perspective can notably influence studying correlators and mutual information under diverse holographic settings, facilitating advances in decoding spacetime correlations.

In sum, this exploration accentuates the crucial addition of quantum facets to the holographic entanglement framework, setting a necessary stage for continuing investigations into more intricate lower-dimensional or strongly-curved gravitational products and their implications on field-theoretic portrayal of quantum entanglement. Future research directions must examine how these frameworks might generalize across non-conformal or massive field theories, exerting the extended tools in practical models of gauge-to-gravity duality.

This fuller grasp of quantum corrections marks a critical progression in the holographic entanglement domain, expanding theoretical possibilities and practical input towards understanding quantum field dynamics and their interplay with gravitational backdrops.