Magnetic operators in 2D compact scalar field theories on the lattice

Abstract

In lattice compact gauge theories, we must impose the admissibility condition to have well-defined topological sectors. The admissibility condition, however, usually forbids the presence of magnetic operators, and it is not so trivial if one can study the monopole physics depending on the topological term, such as the Witten effect, on the lattice. In this paper, we address this question in the case of 2D compact scalars as it would be one of the simplest examples having analogues of the monopole and the topological term. To define the magnetic operator, we propose the ``excision method,'' which consists of excising lattice links (or bonds) in an appropriate region containing the monopole and defining the dual lattice in a particular way. The size of the excised region is $O(1)$ in lattice units so that the monopole becomes point-like in the continuum limit. We give the lattice derivation of the 't~Hooft anomalies between the electric and magnetic symmetries and also derive the higher-group-like structure related to the Witten effect.

arXiv comment21 pages, 4 figures

References in corpus (20)

• Reading between the lines of four-dimensional gauge theories
• Theta, Time Reversal, and Temperature
• Exploring 2-Group Global Symmetries
• Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
• Non-Invertible Duality Defects in 3+1 Dimensions
• On 2-Group Global Symmetries and Their Anomalies
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Notes on generalized global symmetries in QFT
• Comments on Abelian Higgs Models and Persistent Order
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Modified instanton sum in QCD and higher-groups
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta =\pi$: Critical endpoint behavior
• Modified Villain formulation of abelian Chern-Simons theory
• First-principle simulations of 1+1d quantum field theories at $\theta =\pi$ and spin-chains

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