Eight-Dimensional Topological Gravity and its Correspondence with Supergravity

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.