Laurent Baulieu 1,2
1
Laboratoire de Physique Théorique et Hautes Energies, Université de Paris VI and Paris VII, France
2
Department of Physics, Rutgers University, New Brunswick, NJ 60637, U.S.A.
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Laurent Baulieu JHEP04(2004)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)⊂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 Poincaré 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.
E-print Number: hep-th/0304221
Cited: by |
Refers: to
11.10.Kk Field theories in dimensions other than four
Issue 04 (April 2004)
Received 31 July 2003 , accepted for publication 20 April 2004
Published 12 May 2004
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