Abstract
We discuss the gauging of non-linearly realized symmetries as a method to systematically construct spontaneously broken gauge theories. We focus in particular on galileon fields and, using a coset construction, we show how to recover massive gravity by gauging the galileon symmetry. We then extend our procedure to the special galileon, and obtain a theory that couples a massive spin-2 field with a traceless symmetric field, and is free of pathologies at quadratic order around flat space.
Highlights
Even though our formalism produces the correct degrees of freedom and symmetries, the interactions that we can construct are not limited to be the ghost-free ones of de Rham-Gabadadze-Tolley (dRGT) massive gravity
Focusing on the particular case of the galileon shift symmetry, we have argued that its gauging may be used to investigate infrared completions of galileon theory, the goal being to better understand how massive gravity can be formulated when viewed as a gauge theory for the spontaneously broken diffeomorphism invariance
This requires some physical input since formal consistency only demands that gauge symmetries make a subgroup
Summary
The coset construction [32, 33] is a general and systematic method to derive the low-energy effective action for a set of Goldstone bosons associated with any given symmetry breaking pattern. The 1-forms ωα transform covariantly under all the symmetries, as announced, and are the basic building blocks out of which invariant actions may be constructed, by contracting indices with H-invariant tensors It is often more convenient to work with the Goldstone covariant derivatives ∇aπα, defined by. The language of unitary gauge is not necessarily the most useful one, since depending on the context it may obscure the correct power counting of operators in the derivative expansion.10 For this reason, it is in general good practice to carry out the coset construction keeping all the Goldstones and gauge fields, and only fix unitary gauge after building the action, if so desired. We recognize inside the parenthesis the usual gauge field strength, but which in the spontaneously broken case will in general receive corrections proportional to the Goldstones
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