Abstract
In this paper, we present two novel non-relativistic superalgebras which correspond to supersymmetric extensions of the enlarged extended Bargmann algebra. The three-dimensional non-relativistic Chern–Simons supergravity actions invariant under the aforementioned superalgebras are constructed. The new non-relativistic superalgebras allow to accommodate a cosmological constant in a non-relativistic supergravity theory. Interestingly, we show that one of the non-relativistic supergravity theories presented here leads to the recently introduced Maxwellian exotic Bargmann supergravity when the flat limit ell rightarrow infty is considered. Besides, we show that both descriptions can be written in terms of a supersymmetric extension of the Nappi–Witten algebra or the extended Newton–Hooke superalgebra.
Highlights
The NR version of a three-dimensional CS gravity theory invariant under a particular enlargement of the extended Bargmann algebra [29,30,31,32,33,34,35] was presented in [36]
In this paper, we present two novel non-relativistic superalgebras which correspond to supersymmetric extensions of the enlarged extended Bargmann algebra
We show that the semigroup expansion method [64] allows us to obtain new NR superalgebras and provides with the non-vanishing components of the invariant tensor allowing to construct the corresponding NR CS supergravity actions. Both supersymmetric descriptions allow us to introduce a cosmological constant to a NR supergravity action, only one supersymmetric extension contains a well-defined vanishing cosmological constant limit
Summary
We briefly review the enlarged extended Bargmann algebra considered in [36] and the associated CS gravity theory constructed in the same paper in three spacetime dimensions. Page 3 of 19 1105 terms of the U (1) generators Y1, Y2, and Y3) of the relativistic AdS-L symmetry is necessary to assure a finite and non-degenerate invariant tensor allowing to construct a welldefined NR CS gravity theory in three spacetime dimensions. As it was shown in [36], the EEB algebra (2.1) appears as a contraction of the relativistic algebra (2.2).
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