Gravitational Topological Quantum Field TheoryVersus N=2 D=8 Supergravity
Résumé
In a previous work, it was shown that the8-dimensional topological quantum field theory for a metric and aKalb--Ramond 2-form gauge field determines N=1 D=8 supergravity. It isshown here that, the combination of this TQFT with that of a 3-formdetermines N=2 D=8 supergravity, that is, an untruncated dimensionalreduction of N=1D=11 supergravity. Our construction holds for8-dimensional manifolds with Spin(7) \subset SO(8) holonomy. Wesuggest that the origin of local Poincar'e supersymmetry is thegravitational topological symmetry.