Group field theory
Group field theory is a quantum [field theory] in which the base manifold is taken to be a Lie group. It is closely related to background independent quantum gravity approaches such as loop [quantum gravity], the spin foam formalism and causal dynamical triangulation. Its perturbative expansion can be interpreted as spin foams and simplicial pseudo-manifolds. Thus, its partition function defines a non-perturbative sum over all simplicial topologies and geometries, giving a path integral formulation of quantum spacetime.