Abstract
We discuss the lattice formulation of the 't Hooft surface, that is, the two-dimensional surface operator of a dual variable. The 't Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the 't Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.
Highlights
Topological orders are quantum phases beyond the Landau theory of symmetry breaking [1]
We study the ’t Hooft surface in lattice gauge theory
We focus on the lattice gauge Higgs
Summary
Topological orders are quantum phases beyond the Landau theory of symmetry breaking [1]. The ’t Hooft surface gives the criterion for the confinement of the fractionally charged vortices It plays an essential role in the topological order of Cooper pairs in superconductors [16,22,23] and that of diquarks in color superconductors [17,24,25,26,27]. It might seem impossible to calculate the expectation values of the ’t Hooft operators in a quantitative manner This is possible in lattice gauge theory. It was applied to several lattice simulations [28,29,30,31,32,33,34,35,36,37,38] This can be generalized to higher-dimensional defects, say, the ’t Hooft surface. The Euclidean fourdimensional lattice is considered and the lattice unit is used throughout the paper
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