Toward a mechanism for the emergence of gravity

TL;DR

This paper reviews a mechanism for the emergence of gauge symmetries, including diffeomorphisms, in theories without initial gauge invariance, suggesting a pathway for emergent gravity despite known no-go theorems.

Contribution

It extends a previously introduced mechanism to the emergence of linear diffeomorphisms in tensor field theories, providing insights into emergent gravity and addressing no-go theorems.

Findings

Mechanism successfully applied to tensor theories

Emergent diffeomorphisms circumvent no-go theorems

Supports viability of emergent gravity models

Abstract

One of the main problems that emergent-gravity approaches face is explaining how a system that does not contain gauge symmetries ab initio might develop them effectively in some regime. We review a mechanism introduced by some of the authors for the emergence of gauge symmetries in [JHEP 10 (2016) 084] and discuss how it works for interacting Lorentz-invariant vector field theories as a warm-up exercise for the more convoluted problem of gravity. Then, we apply this mechanism to the emergence of linear diffeomorphisms for the most general Lorentz-invariant linear theory of a two-index symmetric tensor field, which constitutes a generalization of the Fierz-Pauli theory describing linearized gravity. Finally we discuss two results, the well-known Weinberg-Witten theorem and a more recent theorem by Marolf, that are often invoked as no-go theorems for emergent gravity. Our analysis illustrates that, although these results pinpoint some of the particularities of gravity with respect to other gauge theories, they do not constitute an impediment for the emergent gravity program if gauge symmetries (diffeomorphisms) are emergent in the sense discussed in this paper.