Three-dimensional exotic Newtonian supergravity theory with cosmological constant

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.