Gravitational topological quantum field theory versus N=2 D=8 supergravity and its lift to N=1 D=11 supergravity -: art. no. 044

In a previous work, it was shown that the 8-dimensional topological quantum field theory for a metric and a Kalb-Ramond 2-form gauge field determines N = 1 D = 8 supergravity, at least in the fermion quadratic aproximation. It is shown here that, the combination of this TQFT with that of a 3-form determines N = 2 D = 8 supergravity, that is, an untruncated dimensional reduction of N = 1 D = 11 supergravity. Our construction holds for 8-dimensional manifolds with Spin(7) subset of SO(8) holonomy. The relationship between the supergravity and topological actions is shown up to quartic fermionic terms, around a Spin(7) vacuum. This suggests that the origin of local Poincare supersymmetry might be the geometrically well-defined gravitational topological symmetry. We also indicate a mechanism for the lift of the TQFT in higher dimensions, which generates Chern-Simons couplings.