An AdS/CFT Connection between Boltzmann and Einstein

TL;DR

This paper explores how a universal sector of strongly coupled field theories, described by the energy-momentum tensor, is dual to pure gravity in AdS space, linking kinetic solutions to gravitational regularity conditions.

Contribution

It introduces the concept of conservative solutions in the Boltzmann equation that are fully determined by the energy-momentum tensor and connects these to the gravity dual in AdS/CFT.

Findings

Conservative solutions in Boltzmann equation are determined by energy-momentum tensor.

Proposes a regularity condition on energy-momentum tensor for smooth gravity horizons.

Suggests irreversibility may only emerge at long observation time scales.

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.