References & Citations
High Energy Physics - Lattice
Title: Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A lattice gauge theory study
(Submitted on 25 Mar 2024 (this version), latest version 2 Apr 2024 (v2))
Abstract: We study how the symmetry operator of the axial $U(1)$ non-invertible symmetry acts on the 't~Hooft line operator in the $U(1)$ gauge theory by employing the modified Villain-type lattice formulation. We model the axial anomaly by a compact scalar boson, the ``QED axion''. For the gauge invariance, the simple 't~Hooft line operator, which is defined by a line integral of the dual $U(1)$ gauge potential, must be ``dressed'' by the scalar and $U(1)$ gauge fields. The anomalous Ward--Takahashi identity with the dressing factor shows that, when the symmetry operator sweep out a 't~Hooft loop, the loop acquires a surface operator of the $U(1)$ field strength with a correction of a higher cup product. This result appears consistent with the phenomenon observed in the continuum theory. A similar analysis for the axion string operator shows that it is not affected by the symmetry operator.
Submission history
From: Hiroshi Suzuki [view email][v1] Mon, 25 Mar 2024 13:27:39 GMT (34kb)
[v2] Tue, 2 Apr 2024 10:35:40 GMT (35kb)
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