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arXiv · 2210.12967

Fractional topological charge in lattice Abelian gauge theory

Motokazu Abe·Okuto Morikawa·Hiroshi Suzuki
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Abstract

We construct a non-trivial $U(1)/\mathbb{Z}_q$ principal bundle on~$T^4$ from the compact $U(1)$ lattice gauge field by generalizing L\"uscher's constriction so that the cocycle condition contains $\mathbb{Z}_q$ elements (the 't~Hooft flux). The construction requires an admissibility condition on lattice gauge field configurations. From the transition function so constructed, we have the fractional topological charge that is $\mathbb{Z}_q$ one-form gauge invariant and odd under the lattice time reversal transformation. Assuming a rescaling of the vacuum angle $\theta\to q\theta$ suggested from the Witten effect, our construction provides a lattice implementation of the mixed 't~Hooft anomaly between the $\mathbb{Z}_q$ one-form symmetry and the time reversal symmetry in the $U(1)$ gauge theory with matter fields of charge~$q\in2\mathbb{Z}$ when $\theta=\pi$, which was studied by Honda and Tanizaki [J. High Energy Phys. \textbf{12}, 154 (2020)] in the continuum framework.

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Motokazu Abe, Okuto Morikawa, Hiroshi Suzuki. 2022-10-24. Fractional topological charge in lattice Abelian gauge theory. https://arxiv.org/abs/2210.12967

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