Gauge theory in dimension 7.

We first review the notion of a G2—manifold, defined in terms of a principal G2 (“gauge”) bundle over a 7—dimensional manifold, before discussing their relation to supergravity. In a second thread, we focus on associative submanifolds and present their deformation theory. In particular, we elaborate on a deformation problem with coassociative boundary condition. Its space of infinitesimal deformations can be identified with the solution space of an elliptic equation whose index is given by a topological formula. [ABSTRACT FROM AUTHOR]