Three-dimensional exotic Newtonian supergravity theory with cosmological constant

TL;DR

This paper develops a supersymmetric extension of a three-dimensional exotic Newtonian gravity theory, incorporating a cosmological constant, by expanding a known superalgebra and deriving a corresponding supergravity action.

Contribution

It introduces a new non-relativistic superalgebra from expanding the AdS superalgebra and constructs a supergravity theory with a cosmological constant, extending previous Newtonian models.

Findings

The superalgebra is expressed as two copies of the enhanced Nappi-Witten algebra.

The supergravity action includes the extended Newton-Hooke supergravity as a special case.

The theory allows the incorporation of a cosmological constant into Newtonian supergravity.

Abstract

We present a supersymmetric extension of the exotic Newtonian Chern-Simons gravity theory in three spacetime dimensions. The underlying new non-relativistic superalgebra is obtained by expanding the $\mathcal{N}=2$ AdS superalgebra and can be written as two copies of the enhanced Nappi-Witten algebra, one of which is augmented by supersymmetry. We show that the exotic Newtonian superalgebra allows to introduce a cosmological constant to the extended Newtonian supergravity. Interestingly, the obtained supergravity action contains the extended Newton-Hooke supergravity as a sub-case.