MG15 - Talk detail

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Abstract

Gravity theories with fixed nondynamical backgrounds explicitly break diffeomorphism and local Lorentz symmetry. However, to maintain observer independence the action describing such theories must still be invariant under general coordinate transformations and changes of local Lorentz bases. This requirement of maintaining general covariance imposes constraints that have the form of Noether identities, but where their interpretation differs from the usual case with dynamical fields. The constraints are either satisfied by additional modes that are present due to the loss of local symmetries, or alternatively Stuckelberg fields can be introduced that restore the broken symmetries and satisfy the Noether identities as dynamical fields. However, in some cases, the constraints cannot be satisfied, and the theories are therefore inconsistent. An examination is made of the compatibility issues between the constraints arising from general covariance, the choice of coordinates and local Lorentz frames, and the solutions for the metric and vierbein. It is then shown how the Stuckelberg approach can satisfy these issues when solutions exist. As a specific example, massive gravity with a fixed nondynamical background is used to illustrate these results.

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