Eight-Dimensional Topological Gravity and its Correspondence with Supergravity
Laurent Baulieu, Marc Bellon, Alessandro Tanzini (LPTHE, Paris VI-VII)

TL;DR
This paper constructs an eight-dimensional topological gravity theory using octonionic self-duality, linking it to supergravity and special holonomy manifolds, revealing new geometric and physical insights.
Contribution
It introduces a topological gravity model in eight dimensions based on octonionic self-duality, connecting it to twisted supergravity and special holonomy geometries.
Findings
The theory is formulated on manifolds with G_2 or Spin(7) holonomy.
A correspondence between the topological gravity and twisted supergravity is established.
The model demonstrates symmetry breaking and recovery similar to topological Yang-Mills theory.
Abstract
A topological theory for euclidean gravity in eight dimensions is built by enforcing octonionic self-duality conditions on the spin connection. The eight-dimensional manifold must be of a special type, with G_2 or Spin(7) holonomy. The resulting theory is related to a twisted version of N=1, D=8 supergravity. The situation is comparable to that of the topological Yang--Mills theory in eight dimensions, for which the SO(8) invariance is broken down to Spin(7), but is recovered after untwisting the topological theory.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Noncommutative and Quantum Gravity Theories · Quantum and Classical Electrodynamics
