Supergravity and the knitting of the Kalb–Ramond two-form in eight-dimensional topological gravity

Topological Euclidean gravity is built in eight dimensions for manifolds with Spin(7)⊂SO(8) holonomy. In a previous work, we considered the construction of an eight-dimensional topological theory describing the graviton and one graviphoton. Here we solve the question of determining a topological model for the combined system of a metric and a Kalb–Ramond two-form gauge field. We then recover the complete N=1, D=8 supergravity theory in a twisted form. We observe that the generalized self-duality conditions of our model correspond to the octonionic string equations.