Asymptotic behavior of large polygonal Wilson loops in confining gauge theories

TL;DR

This paper investigates the asymptotic behavior of large polygonal Wilson loops in confining gauge theories using effective string theory and conformal transformations, validating results with lattice simulations.

Contribution

It introduces a method to compute ratios of polygonal Wilson loops via Laplace determinants, linking EST predictions with lattice Monte Carlo results for hexagons.

Findings

Perfect agreement between EST and lattice MC for large hexagon Wilson loops.

Ratios of polygonal Wilson loops are independent of the gauge group.

Laplace determinants effectively describe asymptotic Wilson loop behavior.

Abstract

In the framework of effective string theory (EST), the asymptotic behavior of a large Wilson loop in confining gauge theories can be expressed via Laplace determinant with Dirichlet boundary condition on the Wilson contour. For a general polygonal region, Laplace determinant can be computed using the conformal anomaly and Schwarz-Christoffel transformation. One can construct ratios of polygonal Wilson loops whose large-size limit can be expressed via computable Laplace determinants and is independent of the (confining) gauge group. These ratios are computed for hexagon polygons both in EST and by Monte Carlo (MC) lattice simulations for the tree-dimensional lattice Z2 gauge theory (dual to Ising model) near its critical point. For large hexagon Wilson loops a perfect agreement is observed between the asymptotic EST expressions and the lattice MC results.