Viscosity Bound Violation in Higher Derivative Gravity (0712.0805v3)

Abstract: Motivated by the vast string landscape, we consider the shear viscosity to entropy density ratio in conformal field theories dual to Einstein gravity with curvature square corrections. After field redefinitions these theories reduce to Gauss-Bonnet gravity, which has special properties that allow us to compute the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning of the coupling, the value of the shear viscosity to entropy density ratio can be adjusted to any positive value from infinity down to zero, thus violating the conjectured viscosity bound. At linear order in the coupling, we also check consistency of four different methods to calculate the shear viscosity, and we find that all of them agree. We search for possible pathologies associated with this class of theories violating the viscosity bound.

• The paper demonstrates that higher derivative corrections can violate the KSS viscosity bound by tuning the Gauss-Bonnet coupling.
• It employs real-time AdS/CFT techniques and stress tensor correlator calculations to derive the η/s ratio for black brane solutions.
• The study reveals implications for gauge/gravity duality while addressing potential causality and consistency issues in modified gravity theories.

Overview of "Viscosity Bound Violation in Higher Derivative Gravity"

This paper investigates the violation of the conjectured viscosity bound in higher derivative gravity theories. Focusing primarily on theories related to the AdS/CFT correspondence, the authors extend previous work concerning induced metrics on the boundary of AdS spacetimes by taking into account higher derivative terms. They aim to understand whether the addition of these terms, specifically Gauss-Bonnet corrections, can result in a violation of the well-known Kovtun-Starinets-Son (KSS) viscosity bound, represented by the ratio $\eta/s = 1/(4\pi)$.

Methodology and Key Findings

The analysis is rooted in a detailed examination of black brane solutions within the framework of Gauss-Bonnet gravity. The authors employ calculations of shear viscosity using various methods, including evaluating the retarded correlator of the stress-energy tensor and drawing from real-time AdS/CFT techniques. A significant aspect of their methodology is examining how field redefinitions allow them to simplify the problem and focus on the influence of specific curvature-square corrections.

One of the paper's major results is an explicit derivation showing that the viscosity-to-entropy density ratio $\eta/s$ can drop below $1/(4\pi)$ by modifying the Gauss-Bonnet coupling. Specifically, they demonstrate that by tuning this coupling, the ratio can range from infinity to zero. Numerically, for the specific case of Gauss-Bonnet gravity, they find the corrected ratio to be $\eta/s = (1 - 4 \lambda_{GB})/(4\pi)$, revealing that the bound is violated as $\lambda_{GB}$ becomes positive. The authors verify this result using multiple approaches, including examining diffusion constants and the properties of quasinormal modes.

Implications and Discussion

The theoretical implications of these findings are profound. By demonstrating a violation of the KSS bound with higher derivative corrections, this research challenges one of the key tenets believed to underpin the phenomenological universality observed in diverse strongly-coupled systems. As such, it opens avenues for refining our understanding of gauge/gravity dualities, potentially reshaping our perspectives on the limitations of holographic theories.

Furthermore, the paper examines possible pathologies associated with theories violating the viscosity bound. The authors explore scenarios, such as issues with causality or unitarity, that might render some of these gravity theories inconsistent. They discuss constraints that could arise in constructing consistent quantum gravitational theories when violating the KSS bound and point towards the prospect of utilizing field theoretical proof strategies to uphold the validity of the bound. As a result, while the violation introduces interesting theoretical questions, the exploration of potential issues ensures the discussion remains grounded in physical viability.

Future Directions

The research presented in this paper invites multiple future directions. Theoretical pursuit of consistent extensions of the existing models in string theory or the landscape of possible quantum gravitational theories becomes a tantalizing possibility. Moreover, additional higher derivative corrections beyond curvature-square terms (e.g., including cubic or quartic corrections) could be considered to further probe the robustness and generalizability of these results.

Understanding the potential observable consequences of such viscosity violations in real-world strongly correlated systems remains a frontier both in quantum field theory and experimental physics, where the realization of systems exhibiting minimal fluidity could provide empirical touchstones for theoretical predictions.

Overall, by probing the deeper structure of higher derivative theories and questioning the foundations of the viscosity bound, the paper contributes significantly to the literature on holography and strongly coupled systems, paving the way for new insights into the dual nature of gravity and field theories.