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arXiv · 2402.02195

Operator Dimension Parity Fractionalization

Christopher W. Murphy
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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.

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Christopher W. Murphy. 2024-02-03. Operator Dimension Parity Fractionalization. https://doi.org/10.1007/jhep01(2025)196

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