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<p>We study novel conformal twist defects in 4d Maxwell theory, around which electric and magnetic fields are exchanged. These are codimension-2 defects living at the end of topological defects for certain non-invertible global symmetries. We determine the operator spectrum of the twist defect by solving classical electromagnetic wave equations subject to a twisted boundary condition. Using techniques from defect CFT, we show that correlation functions of these defect operators factorize into two sectors: a universal generalized free-field sector, and a chiral current sector analogous to edge modes in Chern-Simons theory. In a similar setup, we also revisit the twist fields attached to non-invertible line defects in the 2d compact boson CFT. We discuss a defect ’t Hooft anomaly involving a chiral <i>O</i>(2) symmetry, highlighting its dynamical implications.</p>

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Where non-invertible symmetries end: twist defects for electromagnetic duality

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  • 出版模式：

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  • 发表日期：

    2026年1月19日

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  • Shu-Heng Shao,
  • Siwei Zhong

摘要

We study novel conformal twist defects in 4d Maxwell theory, around which electric and magnetic fields are exchanged. These are codimension-2 defects living at the end of topological defects for certain non-invertible global symmetries. We determine the operator spectrum of the twist defect by solving classical electromagnetic wave equations subject to a twisted boundary condition. Using techniques from defect CFT, we show that correlation functions of these defect operators factorize into two sectors: a universal generalized free-field sector, and a chiral current sector analogous to edge modes in Chern-Simons theory. In a similar setup, we also revisit the twist fields attached to non-invertible line defects in the 2d compact boson CFT. We discuss a defect ’t Hooft anomaly involving a chiral O(2) symmetry, highlighting its dynamical implications.