Investigations into the relationship between loop quantum gravity and string theory

A direct description of quantum gravity, which limits to Einstein's gravity at low energies, is one of the biggest open problems in physics. Two most prominent approaches are string theory, which has the proper low energy perturbative limit but lacks a full non-perturbative quantum gravity formulation, and loop quantum gravity, which is a non-perturbative and background independent quantum theory of holonomies of Ashtekar connections but has yet to reproduce classical general relativity. Various string dualities indicate that different string theories are all unified in a non-perturbative way by a more fundamental M-theory. It turns out that a long wavelength action of topological M theory expressed in terms of three forms reduces to 4-dimensional self-dual loop quantum gravity. It is then enticing to conjecture a duality between loop quantum gravity and string theory, to which we summarize the progress in this direction along with future outlooks.