Exceptional nonrelativistic effective field theories with enhanced symmetries

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