Causality of Holographic Hydrodynamics (0906.2922v3)

Abstract: We study causality violation in holographic hydrodynamics in the gauge theory/string theory correspondence, focussing on Gauss-Bonnet gravity. The value of the Gauss-Bonnet coupling is related to the difference between the central charges of the dual conformal gauge theory. We show that, when this difference is sufficiently large, causality is violated both in the second-order truncated theory of hydrodynamics, as well as in the exact theory. We find that the latter provides more stringent constraints, which match precisely those appearing in the CFT analysis of Hofman and Maldacena.

Causality of Holographic Hydrodynamics

The paper "Causality of Holographic Hydrodynamics" explores causality violations in holographic hydrodynamics, specifically within the context of the gauge/string duality involving Gauss-Bonnet (GB) gravity. It scrutinizes the conditions under which causality violations emerge in strongly coupled fluid dynamics described by the AdS/CFT correspondence. The authors focus on examining the implications of the Gauss-Bonnet coupling, a crucial parameter linking the central charges of the dual conformal field theory (CFT), on causality within these theories.

Summary of Findings

The key contributions of the paper include a detailed analysis of causality violations in both second-order truncated hydrodynamics and the exact hydrodynamic description through the paper of quasinormal modes within the gravitational dual. The investigation is framed by a discussion on the limits of validity for the Gauss-Bonnet coupling constant $\lambda$, revealing that significant deviations between the central charges of the dual CFT cause causality violations.

1. Second-order Truncated Hydrodynamics:
   • The paper initiates with an evaluation of causality in the second-order hydrodynamic framework of GB gravity.
   • It establishes constraints on the relaxation time $\tau_\Pi$, linking it with the shear viscosity to entropy density ratio $\eta/s$, and demonstrates that causality is preserved only when the Gauss-Bonnet coupling $\lambda$ lies within a specific range.
   • Causality constraints for this truncated hydrodynamic model were identified as $-0.711 \leq \lambda \leq 0.113$.
2. Exact Theory Analysis:
   • Extending beyond the truncated models, the paper discusses causality in the full non-linear hydrodynamic setting by analyzing quasinormal modes describing fluctuations of black holes in GB gravity.
   • These analyses imply more stringent conditions for $\lambda$: $-0.194 \leq \lambda \leq 0.09$.
   • Notably, modes in the sound channel, rather than shear modes, impose more significant constraints on causality due to the velocity constraints in the infinite momentum limit.

Implications and Future Prospects

The findings in this paper provide crucial insights into the understanding of hydrodynamic behavior in holographic setups, offering essential conditions for the preservation of causality-related features in strongly coupled quantum fields. This investigation not only strengthens theoretical underpinnings in gauge/gravity duality but also guides numerical simulations of fluid dynamics at strong coupling, which often implicitly work under the small-scale limits of hydrodynamics.

The ramifications of these constraints extend to the continued investigation of the role of higher derivative corrections in gravitational actions, which are becoming increasingly significant in discussing the universality of properties like the $\eta/s$ bound. The research opens pathways for further exploration into holographic duals involving more complicated gravitational theories, including possible cubic or higher curvature corrections, and their impact on the structural integrity of the dual field theories.

Moreover, future studies could potentially delve into the implications of these causal bounds on more phenomenologically relevant scenarios, such as those encountered in heavy-ion collisions described by QCD, pushing the boundaries of theoretical physics toward tangible, real-world applications within the framework of the AdS/CFT correspondence.