Consistent truncation of d = 11 supergravity on AdS_4 x S^7

TL;DR

This paper analyzes the conditions for consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7, clarifying flux ansatze and filling gaps in previous proofs using E_7(7) symmetry.

Contribution

It provides the most general solutions to the truncation equations at each point on the E_7(7)/SU(8) coset, enhancing understanding of fluxes in supergravity.

Findings

Explicit non-linear flux ansatze clarified.

Gaps in the original proof of truncation filled.

Examples illustrating the results provided.

Abstract

We study the system of equations derived twenty five years ago by B. de Wit and the first author [Nucl. Phys. B281 (1987) 211] as conditions for the consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 to gauged N = 8 supergravity in four dimensions. By exploiting the E_7(7) symmetry, we determine the most general solution to this system at each point on the coset space E_7(7)/SU(8). We show that invariants of the general solution are given by the fluxes in eleven-dimensional supergravity. This allows us to both clarify the explicit non-linear ansatze for the fluxes given previously and to fill a gap in the original proof of the consistent truncation. These results are illustrated with several examples.