Resonant superalgebras and [formula omitted] supergravity theories in three spacetime dimensions

Patrick Concha,Remigiusz Durka,Evelyn Rodríguez

doi:10.1016/j.physletb.2020.135659

Abstract

We explore N=1 supersymmetric extensions of algebras going beyond the Poincaré and AdS ones in three spacetime dimensions. Besides reproducing two known examples, we present new superalgebras, which all correspond to supersymmetric extensions with one fermionic charge Qα concerning the so-called resonant algebras being characterized by the presence of an additional bosonic generator Za. We point out particular requirements that superalgebras have to satisfy to be successfully incorporated within valid supergravity actions. The presented algebraic and Lagrangian framework helps us better understand the relations between the various supergravity and supersymmetric Chern-Simons actions invariant under diverse resonant superalgebras.

Highlights

It is well known that three-dimensional supergravity theory [1] with the presence of cosmological constant can be described by the means of the Chern-Simons (CS) action and AdS superalgebra [2]
The additional gauge field appearing for the Maxwell algebra modifies the vacuum of the theory and the asymptotic sector [41]
It was shown that the minimal massive three-dimensional gravity [42] could be seen as a particular case of a generalized minimal massive gravity theory, which appears as a spontaneous breaking of a local symmetry of the CS gravity invariant under the Maxwell algebra [43]

Summary

Introduction

It is well known that three-dimensional supergravity theory [1] with the presence of cosmological constant can be described by the means of the Chern-Simons (CS) action and AdS superalgebra [2]. The expansion procedure based on the semigroups has been of particular interest in gravity context since it allows us to obtain novel algebras from a known one and provides us the non-vanishing components of the invariant tensor crucial for the construction of CS and BI actions. It was shown in [80] that the Maxwell and Soroka-Soroka algebras are not the only algebras that can be obtained as the resonant expansion of the AdS algebra.

Poincare and AdS supergravities

Supersymmetric extensions of the resonant algebras

Supergravity and supersymmetric actions based on resonant superalgebras

C41 C42 B4 C4 B4

Flat limit and Inonu-Wigner contraction

Conclusions