Towards New Membrane Flow From De Wit–nicolai Construction

Abstract

The internal 4-form field strengths with 7-dimensional indices have been constructed by de Wit and Nicolai in 1986. They are determined by the following six quantities: the 56-bein of 4-dimensional N = 8 gauged supergravity, the Killing vectors on the round seven-sphere, the covariant derivative acting on these Killing vectors, the warp factor, the field strengths with 4-dimensional indices and the 7-dimensional metric.In this paper, by projecting out the remaining mixed 4-form field strengths in 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 nonsupersymmetric SO(7) + point, we reproduce the corresponding 11-dimensional uplifts by computing the full nonlinear expressions. Moreover, we find out the 11-dimensional lift of the nonsupersymmetric SO(7) + invariant flow. We decode their implicit formula for the first time and the present work will provide how to obtain the new supersymmetric or nonsupersymmetric membrane flows in 11 dimensions.

Consistent truncation of d = 11 supergravity on AdS 4 × S 7

“…For a partial list of references, see[9][10][11][12][13][14][15][16][17] 2. Recently, a similar inconsistency for the SO(7) + point was independently observed in[22].…”

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