Exceptional nonrelativistic effective field theories with enhanced symmetries

TL;DR

This paper classifies nonrelativistic effective field theories for Nambu-Goldstone bosons with enhanced symmetries, constructing new classes of exceptional theories exhibiting higher-order soft limits and novel Wess-Zumino terms.

Contribution

It introduces a framework for nonrelativistic EFTs with redundant symmetries and constructs explicit nonrelativistic multi-Galileon and multi-flavor DBI theories with unique features.

Findings

Constructed nonrelativistic multi-Galileon theories with enhanced soft limits.

Developed nonrelativistic multi-flavor DBI theories with novel Wess-Zumino terms.

Demonstrated compatibility of Galileon and DBI symmetries with quadratic NG mode dispersion.

Abstract

We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for "exceptional" theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler's zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincare, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.