Group field theories for all loop quantum gravity

Understand

Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism.

• States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence.
• On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs.
• In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space.