Galilean Gauge Theories from Null Reductions

Abstract

The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3 and 4. Different non-relativistic conformal symmetries arise in these contexts: Schr{ö}dinger symmetry in $d=3$ and Galilean conformal symmetry in $d=4$. A canonical analysis further reveals that the symmetries enhance to their infinite dimensional versions in phase space and pick up central extensions. In addition, for the Abelian theory, we discuss non-relativistic electro-magnetic duality in $d=3$ and its difference with the $d=4$ version. We also mention some quantum aspects for both Abelian and non-Abelian theories.

43 pages, various figures

References in corpus (18)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Non-relativistic holography
• The BMS/GCA correspondence
• Nonrelativistic conformal field theories
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Galilean Conformal Algebras and AdS/CFT
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Entanglement entropy in Galilean conformal field theories and flat holography
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Conformal Carroll groups
• Field Theories with Conformal Carrollian Symmetry
• Galilean Isometries
• Galilean Conformal Electrodynamics
• General algorithm for non-relativistic diffeomorphism invariance
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Galilean Electrodynamics: Covariant formulation and Lagrangian

Cited by in corpus (1)

• Supersymmetric Galilean Electrodynamics