Quantum geometry from higher gauge theory

Understand

Higher gauge theories play a prominent role in the construction of 4d topological invariants and have been long ago proposed as a tool for 4d quantum gravity.

• The Yetter lattice model and its continuum counterpart, the BFCG theory, generalize BF theory to 2-gauge groups and -- when specialized to 4d and the Poincar\'e 2-group -- they provide an exactly solvable topologically-flat version of 4d general relativity.
• The 2-Poincar\'e Yetter model was conjectured to be equivalent to a state sum model of quantum flat spacetime developed by Baratin and Freidel after work by Korepanov (KBF model).
• This conjecture was motivated by the origin of the KBF model in the theory of 2-representations of the Poincar\'e 2-group.