Associative Submanifolds Research Articles

On topological $M$-theory

We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. Moreover on M ×S 1 the theory naturally reduces to the standard A-model on Calabi-Yau manifold and to a membrane theory localized on special Lagrangian submanifolds. We discuss some properties of topological membrane theory on G2-manifolds. We also generalize our construction to topological p–branes on special manifolds by exploring a relation between vector cross product structures and TFTs.

Deformations of homogeneous associative submanifolds in nearly parallel $G_2$-manifolds

Deformations of homogeneous associative submanifolds in nearly parallel $G_2$-manifolds