Fine structure of the confining string in an analytically solvable 3D model

TL;DR

This paper investigates the detailed structure of confining flux tubes in a 3D U(1) lattice gauge theory, providing high-precision tests of effective string models through analytical and numerical methods.

Contribution

It offers an analytical solution for a 3D U(1) gauge model and tests effective string predictions against numerical data for flux tube properties.

Findings

Quantitative agreement with effective string theory for flux tube width.

Validation of next-to-leading-order corrections in the confining potential.

Dependence of flux tube properties on the mass gap to string tension ratio.

Abstract

In $\mathrm{U(1)}$ lattice gauge theory in three spacetime dimensions, confinement can be analytically shown to persist at all values of the coupling. Furthermore, the explicit predictions for the dependence of string tension $\sigma$ and mass gap $m_0$ on the coupling allow one to tune their ratio at will. These features, and the possibility of obtaining high-precision numerical results via an exact duality map to a spin model, make this theory an ideal laboratory to test the effective string description of confining flux tubes. In this contribution, we discuss our investigation of next-to-leading-order corrections to the confining potential and of the finite-temperature behavior of the flux tube width. Our data provide a very stringent test of the theoretical predictions for these quantities and allow to test their dependence on the $m_0/\sqrt{\sigma}$ ratio.