Operator dimension parity fractionalization

A bstract Lorentz invariant quantum field theories (QFTs) with fermions in four spacetime dimensions (4D) have a ℤ 4 symmetry provided there exists a basis of operators in the QFT where all operators have even operator dimension, d , including those with d > 4. The ℤ 4 symmetry is the extension of operator dimension parity by fermion number parity. If the ℤ 4 is anomaly-free, such QFTs can be related to 3D topological superconductors. Additionally, imposing the ℤ 4 symmetry on the Standard Model effective field theory severely restricts the allowed processes that violate baryon and lepton numbers.