Local supersymmetric extensions of the Poincare and AdS invariant gravity

TL;DR

This paper constructs local supersymmetric extensions of Poincare and AdS invariant gravity in odd dimensions, showing that the maximal super-Poincare algebra leads to a Chern-Simons gauge theory, with connections between models via algebra expansions.

Contribution

It introduces a maximal super-Poincare algebra extension for supersymmetric gravity and relates Poincare and AdS models through algebra expansion techniques.

Findings

Supersymmetric Lagrangian requires maximal super-Poincare algebra.

The resulting action is a Chern-Simons gauge theory.

Poincare and AdS models are connected via algebra expansion.

Abstract

In all the odd dimensions which allow Majorana spinors, we consider a gravitational Lagrangian possessing local Poincare invariance and given by the dimensional continuation of the Euler density in one dimension less. We show that the local supersymmetric extension of this Lagrangian requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. By maximal, we mean that in the right hand side of the anticommutator of the Majorana super charge appear all the possible central charges. The resulting action defines a Chern-Simons gauge theory for the maximal extension of the super-Poincare algebra. In these dimensions, we address the same problem for the AdS invariant gravity and we derive its supersymmetric extension for the minimal super-AdS algebra. The connection between both models is realized at the algebraic level through an expansion of their corresponding Lie super algebras. Within a procedure consistent with the expansion of the algebras, the local supersymmetric extension of the Poincare invariant gravity Lagrangian is derived from the super AdS one.