Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras

Abstract

We show that infinite families of non-relativistic spin-$3$ symmetries in $2+1$ dimensions, which include higher-spin extensions of the Bargmann, Newton-Hooke, non-relativistic Maxwell, and non-relativistic AdS-Lorentz algebras, can be obtained as Lie algebra expansions of two different spin-$3$ extensions of the Nappi-Witten symmetry. These higher-spin Nappi-Witten algebras, in turn, are obtained by means of Inönü-Wigner contractions applied to suitable direct product extensions of $\mathfrak{sl}(3,\mathbb{R})$. Conversely, we show that the same result can be obtained by considering contractions of expanded $\mathfrak{sl}(3,\mathbb{R})$ algebras. The method can be used to define non-relativistic higher-spin Chern-Simon gravity theories in $2+1$ dimensions in a systematic way.

44 pages, typos corrected, references added

References in corpus (23)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Galilean Conformal Algebras and AdS/CFT
• Spacetime Symmetries of the Quantum Hall Effect
• Notes on the BMS group in three dimensions: I. Induced representations
• Expanding Lie (super)algebras through abelian semigroups
• Thermal Hall Effect and Geometry with Torsion
• Generalized Black Holes in Three-dimensional Spacetime
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
• Expansions of algebras and superalgebras and some applications
• A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
• Deformations of Maxwell algebra and their Dynamical Realizations
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions

Cited by in corpus (6)

• Higher-spin gauge theories in three spacetime dimensions
• Extended Kinematical 3D Gravity Theories
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Three-dimensional non-relativistic Hietarinta supergravity
• Maxwell Chern-Simons gravity in 3D: Thermodynamics of cosmological solutions and black holes with torsion