Conformal Description of Near-Horizon Vacuum States

TL;DR

This paper proposes a conformal field theory framework to describe large spacetime fluctuations near horizons, linking metric fluctuations to entanglement entropy and providing evidence from various models.

Contribution

It introduces a novel conformal description of near-horizon vacuum states and connects metric fluctuations to entanglement entropy in flat, dS, and AdS spaces.

Findings

Fluctuations in the modular Hamiltonian equal entanglement entropy.

Evidence from Randall-Sundrum II braneworld supports the conjecture.

Conformal description applies to flat space, dS horizon, and AdS Ryu-Takayanagi diamonds.

Abstract

Motivated by recent work suggesting observably large spacetime fluctuations in the causal development of an empty region of flat space, we conjecture that these metric fluctuations can be quantitatively described in terms of a conformal field theory of near-horizon vacuum states. One consequence of this conjecture is that fluctuations in the modular Hamiltonian $\Delta K$ of a causal diamond are equal to the entanglement entropy: $\langle \Delta K^2 \rangle = \langle K \rangle = \frac{A(\Sigma_{d-2})}{4 G_d}$, where $A(\Sigma_{d-2})$ is the area of the entangling surface in $d$ dimensions. Our conjecture applies to flat space, the cosmological horizon of dS, and AdS Ryu-Takayanagi diamonds, but not to large finite area diamonds in the bulk of AdS. We focus on three pieces of quantitative evidence, from a Randall-Sundrum II braneworld, from the conformal description of black hole horizons, and from the fluid-gravity correspondence. Our hypothesis also suggests that a broader range of formal results can be brought to bear on observables in flat and dS spaces.