Corner contributions to holographic entanglement entropy

Abstract: The entanglement entropy of three-dimensional conformal field theories contains a universal contribution coming from corners in the entangling surface. We study these contributions in a holographic framework and, in particular, we consider the effects of higher curvature interactions in the bulk gravity theory. We find that for all of our holographic models, the corner contribution is only modified by an overall factor but the functional dependence on the opening angle is not modified by the new gravitational interactions. We also compare the dependence of the corner term on the new gravitational couplings to that for a number of other physical quantities, and we show that the ratio of the corner contribution over the central charge appearing in the two-point function of the stress tensor is a universal function for all of the holographic theories studied here. Comparing this holographic result to the analogous functions for free CFT's, we find fairly good agreement across the full range of the opening angle. However, there is a precise match in the limit where the entangling surface becomes smooth, i.e., the angle approaches $\pi$, and we conjecture the corresponding ratio is a universal constant for all three-dimensional conformal field theories. In this paper, we expand on the holographic calculations in our previous letter arXiv:1505.04804, where this conjecture was first introduced.

• The paper examines corner contributions to holographic entanglement entropy in 3D CFTs, analyzing how higher curvature terms in bulk gravity affect these contributions.
• It finds that the functional form of entropic corner contributions remains universal, with higher curvature modifications only altering multiplicative factors.
• The ratio of the universal corner charge to the central charge appears potentially universal across a broad range of holographic CFT models studied.

Insights on Holographic Entanglement Entropy and Corner Contributions

The paper in question offers a detailed examination of holographic entanglement entropy within three-dimensional conformal field theories (CFTs), with a specific focus on the contributions arising from corners in the entangling surface. The authors, Bueno and Myers, build upon earlier work to explore the implications of higher curvature interactions in the bulk gravity theory, providing a nuanced understanding of how these interactions adjust the entanglement entropy.

The corner contributions to entanglement entropy are renowned for their universal nature and play a significant role in conformal field theories, serving as a critical probe into the structure of these theories. This work focuses on evaluating these contributions within a holographic framework, utilizing the AdS/CFT correspondence to derive the entropic functions and examine their sensitivity to bulk gravitational modifications.

Key Findings and Calculations

1. Universal Structure of Corner Contributions: The analysis concludes that for the range of holographic models considered, the functional form of the entropic corner contributions remains invariant under modifications due to higher curvature terms in the bulk. The changes manifest only as overall multiplicative factors, preserving the dependence on the opening angle.
2. Comparative Analysis of Charges: A comparative assessment of the corner contribution in relation to other physical quantities, such as thermal entropy and stress tensor, reveals that the ratio of the universal corner charge to the central charge in the two-point stress tensor correlator is consistent across the holographic models explored. This indicates the potential universality of this ratio for a broad category of holographic CFTs.
3. Influence of Higher Curvature Gravities: Exploring models extending beyond classic Einstein gravity, such as those incorporating curvature-squared terms and generalized Lovelock gravities, offers insights into the impact of these terms on boundary stress-energy correlators and universal entropic terms.
4. Numerical Validation: The paper reinforces its theoretical assertions with numerical evaluations which indicate excellent quantitative agreement between holographically derived corner functions and those obtained from free field theory calculations for free bosons and fermions, reinforcing the comparison's validity.

Implications and Future Directions

The methodology and findings of this paper implicate future research in several critical ways:

• Universal Constants: The confirmation of the ratio of corner charges over central charges as a universal constant within the field of three-dimensional CFTs opens avenues for further examination in higher-dimensional theories, potentially enriching our understanding of holographic dualities.
• Effects of Curvature Modifications: While the paper largely evidences deviations only in magnitude rather than functional dependence, there remains an open question regarding the effect of even higher order gravitational terms or more exotic geometrical considerations which could affect the holographic surface.
• Further Validation with Diverse Theories: Encounters with unique constants in IR and UV limited cases warrant a broader exploration into interacting models, leveraging techniques from numerical lattice calculations, and dualities in other conformal limits.

In conclusion, Bueno and Myers advance the discourse on understanding entanglement entropy in holographically dual theories, presenting clear pathways for expanding the theoretical toolkit available for future research into quantum gravity, field theory, and beyond. They provide a systematic approach to examining the robustness of entropic measures and pose significant questions for continuity in universal attributes across diverse theoretical landscapes.