Effective field theory for spacetime symmetry breaking
  We discuss the effective field theory for spacetime symmetry breaking from
the local symmetry point of view. By gauging spacetime symmetries, the
identification of Nambu-Goldstone (NG) fields and the construction of the
effective action are performed based on the breaking pattern of diffeomorphism,
local Lorentz, and (an)isotropic Weyl symmetries as well as the internal
symmetries including possible central extensions in nonrelativistic systems.
Such a local picture distinguishes, e.g., whether the symmetry breaking
condensations have spins and provides a correct identification of the physical
NG fields, while the standard coset construction based on global symmetry
breaking does not. We illustrate that the local picture becomes important in
particular when we take into account massive modes associated with symmetry
breaking, whose masses are not necessarily high. We also revisit the coset
construction for spacetime symmetry breaking. Based on the relation between the
Maurer-Cartan one form and connections for spacetime symmetries, we classify
the physical meanings of the inverse Higgs constraints by the coordinate
dimension of broken symmetries. Inverse Higgs constraints for spacetime
symmetries with a higher dimension remove the redundant NG fields, whereas
those for dimensionless symmetries can be further classified by the local
symmetry breaking pattern.
