Consistent nonlinear KK reduction of 11d supergravity on AdS(7) x S-4 and self-duality in odd dimensions

We show that there exists a consistent truncation of 11 dimensional supergr avity to the 'massless' fields of maximal (N = 4) 7 dimensional gauged supe rgravity. We find the complete expressions for the nonlinear embedding of t he 7 dimensional fields into the 11 dimensional fields, and check them by r eproducing the d = 7 susy transformation laws from the d = 11 laws in vario us sectors. In particular we determine explicitly the matrix U which connec ts the Killing spinors to the gravitinos in the KK ansatz, and the dependen ce of the 4-index field strength on the scalars. This is the first time a c omplete nonlinear KK reduction of the original d=11 supergravity on a nontr ivial compact space has been explicitly given. We need a first order formul ation for the 3 index tensor field A(Lambda Pi Sigma) in d = 11 to reproduc e 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 gau ged supergravity (without further massive modes) to compute certain correla tors in the d=6(0,2) CFT at leading order in N. This eliminates an ambiguit y in the formulation of the correspondence. (C) 1999 Published by Elsevier Science B.V. All rights reserved.