Notophs of N = 8 supergravity

Abstract

We study the tensor gauge fields ("notophs") of ungauged N=8 D=4 supergravity in superspace. These are described by 2-form potentials in the adjoint representation of G=E(7(+7)). The consistency of the natural candidates for the superspace constraints for their field strengths fixes the form of the generalized Bianchi identities and also requires the potentials with indices of G/H=E(7(+7))/SU(8) generators to be dual to the scalars of the N=8,D=4 supergravity multiplet. In contrast, the field strengths of the 2-form potentials corresponding to the SU(8) generators are dual to fermionic bilinears, so that these potentials are auxiliary rather than physical fields. Their presence, however, is essential to formulate a tensor hierarchy of N=8,D=4 supergravity consistent with its U-duality group E(7(+7)).