Operator Dimension Parity Fractionalization

Abstract

Lorentz invariant quantum field theories (QFTs) with fermions in four spacetime dimensions (4D) have a ${\mathbb{Z}}_4$ 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 ${\mathbb{Z}}_4$ symmetry is the extension of operator dimension parity by fermion number parity. If the ${\mathbb{Z}}_4$ is anomaly-free, such QFTs can be related to 3D topological superconductors. Additionally, imposing the ${\mathbb{Z}}_4$ symmetry on the Standard Model effective field theory severely restricts the allowed processes that violate baryon and lepton numbers.

v2: 11 pages, 1 figure; JHEP version

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