Effective field theory for spacetime symmetry breaking

TL;DR

This paper develops an effective field theory framework for spacetime symmetry breaking, emphasizing the importance of a local symmetry perspective to correctly identify Nambu-Goldstone fields and incorporate massive modes.

Contribution

It introduces a local symmetry-based approach to spacetime symmetry breaking, improving upon the standard coset construction by accounting for massive modes and symmetry breaking patterns.

Findings

Local symmetry approach clarifies NG field identification.

Massive modes can have low masses, affecting effective theories.

Classification of inverse Higgs constraints based on symmetry dimension.

Abstract

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.