2022/10/24 by Motokazu Abe, Abe, Motokazu, Okuto Morikawa +3
Physics and Astronomy · #Atomic and Subatomic Physics Research #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2210.12967
openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a non-trivial U(1)/ℤq principal bundle on~T4 from the compact U(1) lattice gauge field by generalizing Lüscher's constriction so that the cocycle condition contains ℤq 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 ℤq one-form gauge invariant and odd under the lattice time reversal transformation. Assuming a rescaling of the vacuum angle θ→ qθ suggested from the Witten effect, our construction provides a lattice implementation of the mixed 't~Hooft anomaly between the ℤq one-form symmetry and the time reversal symmetry in the U(1) gauge theory with matter fields of charge~q∈2ℤ when θ=π, which was studied by Honda and Tanizaki [J. High Energy Phys. 12, 154 (2020)] in the continuum framework.