Abstract
In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincaré supergravity in the vanishing cosmological limit. The extension of our results to {mathcal {N}}=p+q supersymmetries is also explored.
Highlights
Teleparallel gravity is an alternative theory of gravity known to be considered equivalent to General Relativity
In this work we have presented a teleparallel supergravity theory in three spacetime dimensions considering the CS formalism
To this end we have first shown that a teleparallel CS gravity action can be constructed using the gauge connection one-form for a particular deformation of the Poincaré algebra, which we have denoted as teleparallel algebra
Summary
Teleparallel gravity is an alternative theory of gravity known to be considered equivalent to General Relativity. The teleparallel formulation of gravity is described by a vanishing curvature and a non-vanishing torsion which characterizes the parallel transport [1,2,3,4,5]. In such case, the geometry is no more Riemannian but corresponds to the so-called Riemannian-Cartan (Weizenböck) geometry. We present a teleparallel CS supergravity theory constructed from a novel superalgebra which can be seen as a supersymmetric extension of a deformed Poincaré algebra.
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