Universality of Gravity from Entanglement

TL;DR

This paper explores how quantum entanglement in conformal field theories underpins the universal nature of gravity, deriving Newton's law and stress-energy sourcing from entanglement properties.

Contribution

It demonstrates that 1/N corrections to the entanglement first law imply that gravity universally couples to stress-energy, linking entanglement to gravitational dynamics.

Findings

Leading 1/N corrections introduce the stress-energy tensor as a source in gravitational equations.

The entanglement first law implies Newton's law of gravitation.

Universality of gravity stems from the universality of entanglement.

Abstract

The entanglement "first law" in conformal field theories relates the entanglement entropy for a ball-shaped region to an integral over the same region involving the expectation value of the CFT stress-energy tensor, for infinitesimal perturbations to the CFT vacuum state. In recent work, this was exploited at leading order in $N$ in the context of large N holographic CFTs to show that any geometry dual to a perturbed CFT state must satisfy Einstein's equations linearized about pure AdS. In this note, we investigate the implications of the leading 1/N correction to the exact CFT result. We show that these corrections give rise to the source term for the gravitational equations: for semiclassical bulk states, the expectation value of the bulk stress-energy tensor appears as a source in the linearized equations. In particular, the CFT first law leads to Newton's Law of gravitation and the fact that all sources of stress-energy source the gravitational field. In our derivation, this universality of gravity comes directly from the universality of entanglement (the fact that all degrees of freedom in a subsystem contribute to entanglement entropy).