Gauging nonrelativistic field theories using the coset construction

Abstract

We discuss how nonrelativistic spacetime symmetries can be gauged in the context of the coset construction. We consider theories invariant under the centrally extended Galilei algebra as well as the Lifshitz one, and we investigate under what conditions they can be supplemented by scale transformations. We also clarify the role of torsion in these theories.Comment: 18 pages, no figures -- typos corrected, matches published versio

Covariant effective action for a Galilean invariant quantum Hall system

“…Our presentation began with flat-space Schrödinger, but the boost transformation of a µ can be seen in many ways. It was demonstrated to be equivalent to Son and Wingate's modified diffeomorphisms in [14] and derived directly from a coset construction on the Bargmann group in this work and others [10,20]. We present the discussion above as an alternate take on what may at first seem a somewhat unnatural description of Newtonian gravity.…”

More on the operator-state map in non-relativistic CFTs

“…It is well-known [1,3,[23][24][25] that coupling a non-relativistic system to a non-trivial gravitational background (geometry) can be achieved by introducing appropriate gauge fields (analogues of metric and connection in general relativity, see Appendix G). Namely, the needed geometric data are the temporal and spatial parts of a vielbein-n µ , e i µ , respectivelyand a gauge field A µ corresponding to the U (1) transformations generated by the particle number operator.…”

Gauge coupling unification without leptoquarks

“…It was introduced initially for treating internal symmetries [33,34], and since then it has been generalized to spacetime symmetries [35][36][37]. For various examples where there has been extensive use of this frameworkespecially in the case of spacetime symmetries-the interested reader is referred to [38][39][40], and references therein.…”