  Inspired by the long wave-length limit of topological M-theory, which
re-constructs the theory of $3+1$D gravity in the self-dual variables'
formulation, we conjecture the existence of a duality between Hilbert spaces,
the ${\bf H}$-duality, to unify topological M-theory and loop quantum gravity
(LQG). By ${\bf H}$-duality non-trivial gravitational holonomies of the
kinematical Hilbert space of LQG correspond to space-like M-branes. The
spinfoam approach captures the non-perturbative dynamics of space-like
M-branes, and can be claimed to be dual to the S-branes foam. The Hamiltonian
constraint dealt with in LQG is reinterpreted as a quantum superposition of
SM-brane nucleations and decays.
