Lattice realization of the axial $U(1)$ non-invertible symmetry

Author:

Yamato Honda, Okuto Morikawa, Soma Onoda, Hiroshi Suzuki

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), High Energy Physics - Theory (hep-th)

journal:

KYUSHU-HET-279, OU-HET-1215

date:

2024-01-02 00:00:00

Abstract

In $U(1)$ lattice gauge theory with compact $U(1)$ variables, we construct the symmetry operator, i.e., the topological defect, for the axial $U(1)$ non-invertible symmetry. This requires a lattice formulation of chiral gauge theory with an anomalous matter content and we employ the lattice formulation on the basis of the Ginsparg--Wilson relation. Then, the invariance of the symmetry operator under the gauge transformation of the gauge field on the defect is realized, imitating the prescription by Karasik in continuum theory, by integrating the lattice Chern--Simons term on the defect over smooth lattice gauge transformations. The projection operator for allowed magnetic fluxes on the defect then automatically emerges with lattice regularization. The resulting symmetry operator is manifestly gauge invariant under lattice gauge transformations.

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