Another supersymmetric extension of local Lorentz symmetry in the vierbein formalism of Einstein gravity

Abstract

A supersymmetric extension of the vierbein formalism of Einstein gravity is investigated by takingSL(N, 2;C) superalgebra, which is shown to be the sole possibility other than the previously investigatedOSp(N 2;C). After general discussion on the ξ-field realization, a non-linear realization of linear representation introduced in a previous paper, it is applied to the fundamental representation ofSL(N, 2;C) t0 which the vierbein supermultiplet belongs. The chiral symmetry derived in the theory is shown to beSO(N) in the same way as in theOSp(N,2;C)-symmetric extension.