2020/08/31 by Tomáš Brauner, Tomas Brauner
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Dispersion relation #Effective field theory #Field (mathematics) #Field theory (psychology) #Homogeneous space #Momentum (technical analysis) #Quadratic equation #Quantum Mechanics and Non-Hermitian Physics #Scattering amplitude #Spacetime #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep02(2021)218
published as JHEP 02 (2021) 218 · 1+40 pages, 1 figure; v2: updated reference list, matches version published in JHEP
openalex created_date 2020/09/01 · openalex publication_date 2021/02/25 · arxiv created 2021/02/28 · arxiv updated 2021/03/16 · openalex updated_date 2026/08/05
A bstract 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 Poincaré, 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.