Non-linear Kaluza-Klein theory for dual fields

TL;DR

This paper develops non-linear uplift ansaetze for all bosonic and dual fields in 7-sphere reductions of D=11 supergravity, providing new insights into Kaluza-Klein theory and its relation to gauged supergravities.

Contribution

It introduces novel non-linear ansaetze for internal components of fluxes and vector fields, expanding the geometric understanding of Kaluza-Klein reductions.

Findings

Constructed a non-linear ansatz for the dual 7-form flux.

Provided ansaetze for all 56 vector fields with new structures.

Reduced generalized vielbein postulates to E7(7) Cartan equation.

Abstract

We present non-linear uplift ansaetze for all the bosonic degrees of freedom and dual fields in the 7-sphere reduction of D=11 supergravity to maximal SO(8) gauged supergravity and test them for the SO$(7)^{\pm}$ invariant solutions. In particular, we complete the known ansaetze for the internal components of the metric and 4-form flux by constructing a non-linear ansatz for the internal components of the dual 7-form flux. Furthermore, we provide ansaetze for the complete set of 56 vector fields, which are given by more general structures than those available from standard Kaluza-Klein theory. The novel features encountered here have no conventional geometric interpretation and provide a new perspective on Kaluza-Klein theory. We study the recently found set of generalised vielbein postulates and, for the 7-sphere compactification, we show that they reduce to the E7(7) Cartan equation of maximal SO(8) gauged supergravity in four dimensions. The significance of this framework for a higher-dimensional understanding of the embedding tensor and other gauged maximal supergravities is briefly discussed.