Three-dimensional teleparallel Chern-Simons supergravity theory

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 $${\mathcal {N}}=p+q$$ N = p + q supersymmetries is also explored.

Three-dimensional non-relativistic extended supergravity with cosmological constant

“…The corresponding NR gravity theory contains a non-vanishing NR torsion in which the cosmological constant can be seen as a source for the curvature of the spatial component of the vielbein. The supersymmetric extension of our theory is also presented by applying the S-expansion to the N = 2 teleparallel superalgebra presented in [16]. As it was shown in [62,63], a particular semigroup allows to reproduce a Galilean expansion providing the respective NR (super)algebra and (super)gravity CS action.…”

“…Moreover, both teleparallel gravity and AdS gravity have identical asymptotic symmetries given by two copies of the Virasoro algebra [9]. Interestingly, three-dimensional teleparallel gravity can be formulated as a gauge theory using the Chern-Simons (CS) formalism and considering the so-called teleparallel algebra [16]. The teleparallel CS gravity action can be alternatively recovered as a particular case of the Mielke-Baelker gravity model [17] by fixing the Mielke-Baelker parameters.…”

“…The teleparallel CS gravity action can be alternatively recovered as a particular case of the Mielke-Baelker gravity model [17] by fixing the Mielke-Baelker parameters. Remarkably, the CS approach allows us to define a supersymmetric teleparallel gravity in the presence of N = p + q supercharges which in the vanishing cosmological constant limit reproduces the N -extended Poincaré supergravity theory [16].…”

“…In this work, we explore the NR counterpart of the teleparellel CS (super)gravity introduced in [16]. In particular, we are interested in studying the role of a non-vanishing torsion in a nonrelativistic environment.…”

“…In particular, we are interested in studying the role of a non-vanishing torsion in a nonrelativistic environment. To this end, we first explore the NR limit of a particular U (1)-enlargement of the teleparallel algebra introduced in [16]. We obtain a torsional NR algebra by applying a proper Inönü-Wigner contraction to the [teleparallel]⊕u (1) 2 algebra.…”