Abstract
We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the non-relativistic limits of the minimal and the mathcal{N} = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.
Highlights
JHEP04(2020)051 found in [52,53,54,55,56,57,58]
We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra
We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators
Summary
We briefly review the Maxwellian extended Bargmann algebra introduced in [74] and the associated CS gravity theory developed in the same paper in three (2+1) dimensions. The CS form constructed with the invariant bilinear form defines an action for the relativistic gauge theory for the symmetry under consideration as ICS =. In the specific case we are reviewing, when the Maxwell algebra is supplemented with the three additional U(1) generators (Y1, Y2, and Y3), the connection one-form involved in the construction reads. In terms of the NR generators and fields, the gauge connection one-form of [74], A =. Let us note that, since the bilinear form does not result to acquire degeneracy in the contraction process, the equations of motion from the NR action (2.10) are given by the vanishing of all the curvatures (2.9)
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