Abstract
We study the confinement between vortex strings in the dual lattice gauge theory of the abelian Higgs model. The dual lattice gauge theory is described by a 2-form gauge field. We calculate the string-antistring potential from the surface operator of the 2-form gauge field. The linear confining potential appears in a confinement phase and it disappears in a deconfinement phase. The phase diagram of the theory is also obtained.
Highlights
A quantum vortex string is a one-dimensional topological soliton
We study the confinement between vortex strings in the lattice gauge theory of the dual Abelian Higgs model
The dual lattice gauge theory is described by a two-form gauge field coupled with a one-form gauge field
Summary
A quantum vortex string is a one-dimensional topological soliton. The existence of vortex strings was experimentally confirmed in superconductors [1] and superfluids [2]. The world sheets of vortex strings are described by the surface operator of a two-form gauge field. This is an analog of the Wilson loop operator in one-form gauge theory. The interaction between the vortex strings can be investigated from the surface operator of the two-form gauge field. The two-form gauge theory can be nonperturbatively formulated by lattice regularization [5,6,7,8,9,10]. The theory exhibits the confinement-deconfinement phase transition of vortex strings. We confirm this based on two analyses. IV, we draw the phase diagram of this theory by calculating a susceptibility
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