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.
Highlights
The pursuit of a theory able to combine the principles of general relativity and quantum mechanics is one of the strongest driving forces in modern fundamental physics
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 are emergent in the sense discussed in this paper
We study the mechanism for the emergence of gauge symmetries and find the emergence of the closest gauge symmetries to diffeomorphisms and WTDiff within this framework
Summary
The pursuit of a theory able to combine the principles of general relativity and quantum mechanics is one of the strongest driving forces in modern fundamental physics. The motivation for this study comes from the observation that it is quite common to find analogues of gravitational fields in many physical systems, especially in condensedmatter systems [6] This analogy just holds at a kinematical level, meaning that the effective geometry emerging in those systems does not display the dynamical features characteristic of general relativity. We do not delve into this problem, which we think arises because of the tacit assumption that the effective field description survives far in the dispersive regime, and just assume the existence of a lowenergy Lorentzian regime This ensures that we can apply the rules of effective field theory and write down the most general effective action compatible with the symmetries of the system in order to obtain a good description of the phenomena of interest [12,13]. We use greek (μ, ν...) indices for the spacetime indices and latin indices (a, b...) for the internal indices of vector fields
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