Holographic GB gravity in arbitrary dimensions (0911.4257v2)

Abstract: We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general $D \ge 5$ dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from the second-order truncated theory of hydrodynamics.

• The paper constructs a holographic dictionary for Gauss-Bonnet gravity by deriving universal couplings that relate gravitational stress tensors to dual CFT correlators.
• It imposes energy flux constraints to guarantee positive energy propagation and causal dynamics in the dual field theory, thereby bounding the Gauss-Bonnet coupling.
• The study extends holographic hydrodynamics to arbitrary dimensions, elucidating how higher-curvature corrections influence transport coefficients such as shear viscosity and relaxation time.

Analysis of "Holographic GB Gravity in Arbitrary Dimensions"

The paper presents a detailed exploration of Gauss-Bonnet (GB) gravity within the context of the AdS/CFT correspondence in arbitrary dimensions $D \geq 5$. It addresses the development of the holographic dictionary necessary for relating gravitational theories to their conformal field theory (CFT) duals, with a particular focus on higher curvature interactions.

Key Contributions and Findings

1. AdS/CFT Dictionary Construction: The paper establishes the AdS/CFT correspondence for GB gravity by calculating universal couplings related to the stress tensor's correlators in the dual CFT. The authors calculate key parameters such as the two-point function central charge $T$, and explore the roles of the three-point function coefficients $A$, $B$, and $C$.
2. Energy Flux Constraints: One of the critical analyses involves computing energy fluxes in scattering processes within the dual CFT. The paper imposes constraints on the GB coupling by requiring positive energy fluxes and the causal propagation of fluctuations in the CFT. These constraints align with the necessity of avoiding causality violations in gravitational theories manifested as superluminal propagation in their duals.
3. Holographic Hydrodynamics: The paper explores holographic hydrodynamics in the context of GB gravity, providing insights into the ratio of shear viscosity to entropy density $\eta/s$, and assessing the constraints on gravitational theories from second-order hydrodynamic analyses. The evaluation of causality violations within this framework extends the understanding of transport coefficients such as relaxation time $\tau_\Pi$.
4. Dimensional Analysis: An interesting aspect of the paper is the extension to arbitrary dimensions, leading to the realization that causality and positivity conditions provide universal constraints on the coupling constants in higher-dimensional gravity theories. This extension facilitates broader theoretical implications for understanding CFTs and their gravitational duals beyond familiar four-dimensional spacetimes.

Theoretical and Practical Implications

• Theoretical Boundaries: The findings reinforce the non-universality of the lower bound $\eta/s \geq 1/4\pi$ under higher curvature corrections, challenging the conjectured universality. The paper outlines specific constraints on the GB coupling, ubiquitously recognized as a measure of higher curvature contributions in string theory contexts.
• Colloquium on Energy Flux Analysis: Interestingly, the research methodically matches constraints derived from energy flux positivity and causality, indicating that constraints drawn from the energy flux positively align with avoiding causality violations. This approach could be compelling for future studies as it suggests a comprehensive method to analyze theoretical consistency in holographic models.
• Future Speculations: As the exploration involves arbitrary spacetime dimensions, it paves the way for extensions in the paper of exotic theories in higher-dimensional physics, potentially contributing to insights in theories like string theory and the broader scope of quantum gravity frameworks.

In summary, the paper contributes substantial theoretical advancements in holographically understanding GB gravity, proposing constraints and making elucidative observations for high-dimensional quantum field theories. Its meticulous analysis on impositions such as causality and flux consistency form a robust base for future theoretical explorations in holography and gravitational physics.