Study of the flux tube thickness in 3d LGT's by means of 2d spin models

TL;DR

This paper investigates the flux tube thickness in 3D lattice gauge theories by mapping the problem to a 2D spin model, deriving explicit expressions, and confirming agreement with effective string predictions.

Contribution

It introduces a novel approach using the Svetitsky-Yaffe conjecture and form factors to analyze flux tube thickness in 3D Lattice Gauge Theories via 2D spin models.

Findings

Explicit expression for <epsilon sigma sigma> correlation function

Flux tube thickness matches effective string theory predictions

Method provides a new way to study confinement phenomena

Abstract

We study the flux tube thickness in the confining phase of the (2+1)d SU(2) Lattice Gauge Theory near the deconfining phase transition. Following the Svetitsky-Yaffe conjecture, we map the problem to the study of the <epsilon sigma sigma> correlation function in the two-dimensional spin model with Z_2 global symmetry, (i.e. the 2d Ising model) in the high-temperature phase. Using the form factor approach we obtain an explicit expression for this function and from it we infer the behaviour of the flux density of the original (2+1)d LGT. Remarkably enough the result we obtain for the flux tube thickness agrees (a part from an overall normalization) with the effective string prediction for the same quantity.