Consistent nonlinear KK reduction of 11d supergravity on $AdS_7\times S_4$ and self-duality in odd dimensions

TL;DR

This paper presents the first explicit nonlinear Kaluza-Klein reduction of 11d supergravity on $AdS_7 imes S_4$, connecting 11d fields to 7d gauged supergravity and exploring self-duality in odd dimensions, with implications for AdS/CFT.

Contribution

It provides the complete nonlinear embedding of 7d supergravity into 11d supergravity, including explicit formulas and the role of first order formalism in odd dimensions.

Findings

Explicit nonlinear KK reduction formulas derived.

Connection between 11d supergravity and 7d gauged supergravity established.

Implications for AdS/CFT correspondence clarified.

Abstract

We show that there exists a consistent truncation of 11 dimensional supergravity to the 'massless' fields of maximal (N=4) 7 dimensional gauged supergravity. We find the complete expressions for the nonlinear embedding of the 7 dimensional fields into the 11 dimensional fields, and check them by reproducing the d=7 susy transformation laws from the d=11 laws in various sectors. In particular we determine explicitly the matrix U which connects the Killing spinors to the gravitinos in the KK ansatz, and the dependence of the 4-index field strength on the scalars. This is the first time a complete nonlinear KK reduction of the original d=11 supergravity on a nontrivial compact space has been explicitly given. We need a first order formulation for the 3 index tensor field $A_{\Lambda\Pi\Sigma}$ in d=11 to reproduce the 7 dimensional result. The concept of 'self-duality in odd dimensions' is thus shown to originate from first order formalism in higher dimensions. For the AdS-CFT correspondence, our results imply that one can use 7d gauged supergravity (without further massive modes) to compute certain correlators in the d=6 (0,2) CFT at leading order in N. This eliminates an ambiguity in the formulation of the correspondence.