Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries

Dmitry Chernyavsky, Dmitri Sorokin

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13 Citations (Scopus)


We show that an extended 3D Schrödinger algebra introduced in [1] can be reformulated as a 3D Poincaré algebra extended with an SO(2) R-symmetry generator and an SO(2) doublet of bosonic spin-1/2 generators whose commutator closes on 3D translations and a central element. As such, a non-relativistic Chern-Simons theory based on the extended Schrödinger algebra studied in [1] can be reinterpreted as a relativistic Chern-Simons theory. The latter can be obtained by a contraction of the SU(1, 2) × SU(1, 2) Chern-Simons theory with a non principal embedding of SL(2, ℝ) into SU(1, 2). The non-relativisic Schrödinger gravity of [1] and its extended Poincaré gravity counterpart are obtained by choosing different asymptotic (boundary) conditions in the Chern-Simons theory. We also consider extensions of a class of so-called l-conformal Galilean algebras, which includes the Schrödinger algebra as its member with l = 1/2, and construct ChernSimons higher-spin gravities based on these algebras.

Original languageEnglish
Article number156
JournalJournal of High Energy Physics
Issue number7
Publication statusPublished - 1 Jul 2019


  • Conformal and W Symmetry
  • Conformal Field Theory
  • Higher Spin Gravity

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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