Notophs of N = 8 supergravity

TL;DR

This paper investigates the properties and roles of tensor gauge fields ('notophs') in N=8 supergravity, revealing their dualities, auxiliary nature, and importance in constructing a consistent tensor hierarchy aligned with U-duality.

Contribution

It provides a detailed superspace analysis of notophs in N=8 supergravity, clarifying their dualities and their necessity for a consistent tensor hierarchy.

Findings

Notophs are described by 2-form potentials in the adjoint of E7(7).

Potentials with G/H indices are dual to scalars, while those with SU(8) indices are dual to fermionic bilinears.

Presence of these potentials is essential for a tensor hierarchy compatible with U-duality.

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)).