Effective string description of the interquark potential in the 3D U(1) lattice gauge theory

TL;DR

This study investigates the confining string in 3D U(1) lattice gauge theory, revealing deviations from Nambu-Goto predictions and confirming the significance of extrinsic curvature effects consistent with Polyakov's theory.

Contribution

The paper provides high-precision numerical tests of the effective string in 3D U(1) gauge theory, demonstrating the role of extrinsic curvature corrections and their scaling behavior.

Findings

Deviations from Nambu-Goto predictions observed.

Extrinsic curvature term fits data well and scales as expected.

Boundary effects influence the effective string behavior.

Abstract

The U(1) lattice gauge theory in three dimensions is a perfect laboratory to study the properties of the confining string. On the one hand, thanks to the mapping to a Coulomb gas of monopoles, the confining properties of the model can be studied semi-classically. On the other hand, high-precision numerical estimates of Polyakov loop correlators can be obtained via a duality map to a spin model. This allowed us to perform high-precision tests of the universal behavior of the effective string and to find macroscopic deviations with respect to the expected Nambu-Goto predictions. These corrections could be fitted with very good precision including a contribution (which is consistent with Lorentz symmetry) proportional to the square of the extrinsic curvature in the effective string action, as originally suggested by Polyakov. Performing our analysis at different values of $\beta$ we were able to show that this term scales as expected by Polyakov's solution and dominates in the continuum. We also discuss the interplay between the extrinsic curvature contribution and the boundary correction induced by the Polyakov loops.