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

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Operator dimension parity fractionalization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月31日

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  • Christopher W. Murphy

摘要

Lorentz invariant quantum field theories (QFTs) with fermions in four spacetime dimensions (4D) have a ℤ4 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 ℤ4 symmetry is the extension of operator dimension parity by fermion number parity. If the ℤ4 is anomaly-free, such QFTs can be related to 3D topological superconductors. Additionally, imposing the ℤ4 symmetry on the Standard Model effective field theory severely restricts the allowed processes that violate baryon and lepton numbers.