Generalized Spin-Statistics Theorem for Loop Excitations

Explore an extended spin-statistics theorem applicable to loops in this BIMSA conference talk. Delve into a novel interpretation using a Klein bottle with twisted framing, expanding the traditional worldline representation of particles. Examine the use of Stiefel-Whitney classes to define fermionic self-statistics of loops and their field theory representations. Discover new exactly solvable local commuting projector lattice Hamiltonian models for beyond group cohomology invertible bosonic topological phases across various spacetime dimensions. Learn about the "w_2 w_3" phase in 4+1D and its anomalous 3+1D boundary topological order. Investigate examples of fermionic loop excitations within 3+1D toric codes and new Pauli stabilizer models in 4+1 dimensions. Gain insights into the theoretical framework advancing the understanding of fermionic loop statistics within topological field theories.