Emergent Gravity requires (kinematic) non-locality

TL;DR

This paper argues that emergent gravity cannot be compatible with local kinematic field theories unless it involves non-locality, due to the boundary nature of gravitational Hamiltonians and the necessity of frozen bulk dynamics.

Contribution

It refines previous arguments by showing that gravitational theories with universal energy coupling must have boundary Hamiltonians, implying non-locality in emergent gravity models.

Findings

Gravitational Hamiltonians are pure boundary terms on shell.

Bulk dynamics must be frozen for low energy effective descriptions.

The result applies to lattice and continuum theories without requiring Lorentz or translation invariance.

Abstract

This work refines arguments forbidding non-linear dynamical gravity from appearing in the low energy effective description of field theories with local kinematics, even for those with instantaneous long-range interactions. Specifically, we note that gravitational theories with universal coupling to energy -- an intrinsically non-linear phenomenon -- are characterized by Hamiltonians that are pure boundary terms on shell. In order for this to be the low energy effective description of a field theory with local kinematics, all bulk dynamics must be frozen and thus irrelevant to the construction. The result applies to theories defined either on a lattice or in the continuum, and requires neither Lorentz-invariance nor translation-invariance.