Abstract
Gauge symmetries remove unphysical states and guarantee that field theories are free from the pathologies associated with these states. In this work we find a set of general conditions that guarantee the removal of unphysical states in field theories describing interacting vector fields. These conditions are obtained through the extension of a mechanism for the emergence of gauge symmetries proposed in a previous article [C. Barcel\'o J. High Energy Phys. 10 (2016) 084] in order to account for non-Abelian gauge symmetries, and are the following: low-energy Lorentz invariance, emergence of massless vector fields describable by an action quadratic in those fields and their derivatives, and self-coupling to a conserved current associated with specific rigid symmetries. Using a bootstrapping procedure, we prove that these conditions are equivalent to the emergence of gauge symmetries and, therefore, guarantee that any theory satisfying them must be equivalent to a Yang-Mills theory at low energies.
Highlights
The search for a theory of quantum gravity, i.e., a theory which combines the principles of general relativity and quantum mechanics, has been one of the key cornerstones in fundamental physics of the last century
In this work we find a set of general conditions that guarantee the removal of unphysical states in field theories describing interacting vector fields
High Energy Phys. 10 (2016) 084] in order to account for non-Abelian gauge symmetries, and are the following: low-energy Lorentz invariance, emergence of massless vector fields describable by an action quadratic in those fields and their derivatives, and self-coupling to a conserved current associated with specific rigid symmetries
Summary
The search for a theory of quantum gravity, i.e., a theory which combines the principles of general relativity and quantum mechanics, has been one of the key cornerstones in fundamental physics of the last century. Other hand, we have approaches in which the fundamental degrees of freedom are not taken to be the spacetime itself but such a concept emerges with all of the properties of general relativity in some regimes of the theory, typically in low-energy limits. Within this category, we would include string theory [3,4], and theories that start from systems akin to a condensed-matter system as the substratum for emergence [5]. We use greek ðμ; ν...Þ indices for the spacetime indices, latin indices from the beginning of the alphabet ða; b...Þ for the internal indices on the space of gauge fields, and from the middle of the alphabet ði; j...Þ for the internal indices within the flavor space of matter fields
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