An AdS/CFT Connection between Boltzmann and Einstein

Abstract

The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor \emph{alone}. We first show that the Boltzmann equation has very special solutions which could be \textit{functionally} completely determined in terms of the energy-momentum tensor alone. We call these solutions \textit{conservative solutions}. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these \textit{conservative solutions} form the universal sector dual to pure gravity at strong coupling and large $N$. Based on this observation, we propose a \textit{regularity condition} on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

42 pages; this contains exactly the same content as the earlier versions but the presentation has been made more concise and readable; some references which are not directly relevant to this work have been removed at the insistence of PRD referees.

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• Time-dependence of the holographic spectral function: Diverse routes to thermalisation
• Holography as a highly efficient RG flow II: An explicit construction
• Quasinormal modes of a semi-holographic black brane and thermalization
• The holographic spectral function in non-equilibrium states
• Homogeneous Relaxation at Strong Coupling from Gravity
• Understanding the holographic principle via RG flow
• Phenomenology of Irreversible Processes from Gravity