Toward a Mechanism for the Emergence of Gravity

This is an Open Access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License (http://creativecommons.org/licenses/by/4.0/).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. © 2021 by the authors.Financial support was provided by the Spanish Government through the projects FIS2017-86497-C2-1-P, FIS2017-86497-C2-2-P, PID2019-107847RB-C44, PID2020-118159GB-C43, PID2020-118159GB-C44, and by the Junta de Andalucia through the project FQM219. C.B. and G.G.M. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709). GGM acknowledges financial support from IPARCOS.Peer reviewe