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

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.