Eight-Dimensional Topological Gravity and its Correspondence with Supergravity

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.

LaTeX file, 9 pages

References in corpus (1)

• Topological Gravity versus Supergravity on Manifolds with Special Holonomy

Cited by in corpus (7)

• Towards an Ashtekar formalism in eight dimensions
• Octonions, G_2 Symmetry, Generalized Self-Duality and Supersymmetries in Dimensions D \le 8
• Self-Dual N=(1,0) Supergravity in Eight Dimensions with Reduced Holonomy Spin(7)
• Self-Dual Supergravity in Seven Dimensions with Reduced Holonomy G_2
• Supergravity and the Knitting of the Kalb--Ramond Two-Form in Eight-Dimensional Topological Gravity
• Symmetries and observables in topological gravity
• Gravitational Topological Quantum Field Theory Versus N = 2 D = 8 Supergravity and its lift to N = 1 D = 11 Supergravity