### Abstract

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 language | English |
---|---|

Article number | 156 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries.** / Chernyavsky, Dmitry; Sorokin, Dmitri.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2019, no. 7, 156. https://doi.org/10.1007/JHEP07(2019)156

}

TY - JOUR

T1 - Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries

AU - Chernyavsky, Dmitry

AU - Sorokin, Dmitri

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - Conformal and W Symmetry

KW - Conformal Field Theory

KW - Higher Spin Gravity

UR - http://www.scopus.com/inward/record.url?scp=85069672749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069672749&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2019)156

DO - 10.1007/JHEP07(2019)156

M3 - Article

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 156

ER -