  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.
