From current algebras for p-branes to topological M-theory

In this note we generalize a result by Alekseev and Strobl for the case of p-branes. We show that there is a relation between anomalous free current algebras and "isotropic" involutive subbundles of T⊕∧pT* with the Vinogradov bracket, that is a generalization of the Courant bracket. As an application of this construction we go through some interesting examples: topological strings on symplectic manifolds, topological membrane on G2-manifolds and topological 3-brane on Spin(7) manifolds. We show that these peculiar topological theories are related to the physical (i.e., Nambu-Goto) brane theories in a specific way. These topological brane theories are proposed as microscopic description of topological M/F-theories.