CONSTRAINTS ON EMERGENT GRAVITY

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 being 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 invariance, but a gravitational theory without fundamental spin 2 gauge invariance must either lack a stress–energy operator or have a nonrelativistic graviton. The latter option is incompatible with the principle of equivalence, though such theories are not necessarily ruled out at low energies.