Constraints on emergent gravity

TL;DR

This paper reviews the challenges in developing a quantum field theory where gravity emerges at low energies, focusing on theoretical constraints like the Weinberg-Witten theorem and their implications for emergent gravity models.

Contribution

It analyzes the constraints imposed by fundamental theorems on emergent gravity theories and discusses the incompatibility of certain approaches with established physical principles.

Findings

Weinberg-Witten theorem restricts emergent gravity models.

Emergent gravity without fundamental spin 2 gauge invariance faces significant challenges.

Non-relativistic gravitons conflict with the principle of equivalence.

Abstract

In this essay we review the central difficulty in formulating a viable quantum field theory in which gravity is emergent at low energies, rather than mediated by a fundamental gauge field. The Weinberg-Witten theorem forbids spin 2 massless modes from carrying Lorentz covariant stress-energy. In General Relativity the stress-energy is not covariant because it violates a gauge symmetry, but a gravitational theory without fundamental spin 2 gauge invariance must either lack a stress-energy operator or have a non-relativistic graviton. The latter option is incompatible with the principle of equivalence, though such theories are not necessarily ruled out at low energies.