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The internal 4-form field strengths with 7-dimensional indices have beenconstructed by de Wit and Nicolai in 1986. They are determined by the followingsix quantities: the 56-bein of 4-dimensional N=8 gauged supergravity, theKilling vectors on the round seven-sphere, the covariant derivative acting onthese Killing vectors, the warp factor, the field strengths with 4-dimensionalindices and the 7-dimensional metric.  In this paper, by projecting out the remaining mixed 4-form field strengthsin an SU(8) tensor that appears in the variation of spin 1/2 fermionic sector,we also write down them explicitly in terms of some of the above quantities.For the known critical points, the N=8 SO(8) point and the nonsupersymmetricSO(7)^{+} point, we reproduce the corresponding 11-dimensional uplifts bycomputing the full nonlinear expressions. Moreover, we find out the11-dimensional lift of the nonsupersymmetric SO(7)^{+} invariant flow. Wedecode their implicit formula for the first time and the present work willprovide how to obtain the new supersymmetric or nonsupersymmetric membraneflows in 11-dimensions.

Towards New Membrane Flow from de Wit-Nicolai Construction