Universal hydrodynamics of non-conformal branes (0901.1487v2)

Abstract: We examine the hydrodynamic limit of non-conformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to non-conformal brane solutions by showing that all such solutions can be obtained from higher dimensional asymptotically locally AdS solutions by suitable dimensional reduction and continuation in the dimension. As a consequence, many holographic results for such backgrounds follow from the corresponding results of the Asymptotically AdS case. In particular, the hydrodynamics of non-conformal branes is fully determined in terms of conformal hydrodynamics. Using previous results on the latter we predict the form of the non-conformal hydrodynamic stress tensor to second order in derivatives. Furthermore we show that the ratio between bulk and shear viscosity is fixed by the generalized conformal structure to be \zeta/\eta = 2(1/(d-1) - c_s^2), where c_s is the speed of sound in the fluid.

• The paper advances hydrodynamic theory by deriving the non-conformal stress tensor through holographic dimensional reduction and continuation from higher-dimensional AdS solutions.
• It demonstrates that non-conformal brane dynamics can be described using conformal hydrodynamics, accurately predicting key quantities like the bulk to shear viscosity ratio.
• The findings pave the way for applying holographic dualities to non-conformal systems, potentially guiding future investigations into multi-dimensional hydrodynamic behavior.

An Examination of the Universal Hydrodynamics of Non-Conformal Branes

The paper "Universal Hydrodynamics of Non-Conformal Branes" by Ingmar Kanitscheider and Kostas Skenderis advances the understanding of hydrodynamic limits of non-conformal branes through the application of an elaborate holographic dictionary. By refining the discussion of holography in relation to non-conformal brane solutions, the research reveals that such solutions can be developed from higher-dimensional asymptotically locally Anti-de Sitter (AdS) solutions via appropriate processes of dimensional reduction and continuation.

Theoretical Framework and Methodology

The foundational aspect of this paper lies in the AdS/CFT correspondence, which furnishes a robust framework to analyze strongly coupled quantum field theories, often in the field of infinite temperature conformal field theories (CFTs). The intrinsic ability of interacting field theories to equilibrate at high densities implies that their long-wavelength fluctuations can be expressed through hydrodynamics. Previous research had demonstrated mapping solutions regarding boosted black D3 brane geometry to hydrodynamic equations within strongly coupled CFTs. Extending this approach, Kanitscheider and Skenderis focus on non-conformal branes, specifically examining backgrounds asymptotically approaching near-horizon limits of Dp-brane and fundamental string solutions.

Hydrodynamics of Non-Conformal Branes

A pivotal result derived in this paper is that the hydrodynamics applicable to non-conformal branes can actually be fully described using conformal hydrodynamics. Their work predicts the non-conformal hydrodynamic stress tensor, accurately computed up to the second derivative order. One significant formulation presented is the ratio between bulk ($\zeta$) and shear ($\eta$) viscosity, dictated by the generalized conformal structure, which remains constant at $\zeta/\eta = 2(1/(d-1) - c_s)$, where $c_s$ is the speed of sound.

Implications and Future Directions

The paper has significant implications both theoretically and practically. Theoretically, it suggests that underlying conformal structures can govern non-conformal systems, indicated by uniformity found in the viscosity ratio. Practically, these insights open new potential pathways in crafting dual models of non-conformal brane systems, encouraging further investigations into the dynamics of non-conformal theories beyond leading order.

Moving forward, the paper of hydrodynamic properties in multi-dimensional theories, especially non-conformal and non-relativistic ones, might uncover novel properties and deepen our understanding of gauge/gravity dualities. Future studies could explore higher derivative corrections, or how these hydrodynamic insights could be applied to real-world plasma systems.

In conclusion, Kanitscheider and Skenderis provide a thorough analysis that not only corroborates existing hydrodynamic predictions regarding non-conformal branes but also extends the theoretical landscape by establishing concrete relationships between non-conformal structures and their higher-dimensional conformal origins. Through detailed analysis and robust theoretical underpinnings, this paper significantly contributes to our comprehensive understanding of hydrodynamics within the framework of holographic dualities.