Complete $D=11$ embedding of SO(8) supergravity
Résumé
The truncation formulas of D=11 supergravity on S7 to D=4 N=8 SO(8)-gauged supergravity are completed to include the full nonlinear dependence of the D=11 three-form potential A^(3) on the D=4 fields, and their consistency is shown. The full embedding into A^(3) is naturally expressed in terms of a restricted version, still N=8 but only SL(8)–covariant, of the D=4 tensor hierarchy. The redundancies introduced by this approach are removed at the level of the field strength F^(4) by exploiting D=4 duality relations. Finally, new expressions for the full consistent truncation formulas are given that are explicit in all D=11 and D=4 fields.