Confining string beyond the free approximation: the case of random percolation

TL;DR

This paper investigates the flux tube in a random percolation model, demonstrating it can be described by an effective string theory, and determines quantum corrections and universal ratios with high precision.

Contribution

It provides a high-precision study of the flux tube in a random percolation model, connecting it to effective string theory and calculating quantum corrections in the continuum limit.

Findings

Flux tube described by effective string theory.

Determined next-to-leading quantum corrections.

Established relation to universal ratio T_c/√σ_0.

Abstract

The random percolation model can be viewed as the dual of a well defined confining gauge theory; since this theory, having no Monte Carlo dynamics at all, is simple to simulate, it is possible to study the properties of the flux tube with very high precision; we show it can be described by the effective string picture. Our results are lattice regularisation independent, therefore they are well defined also in the continuum limit, and, for the first time in a gauge theory, it has been possible to determine the next-to-leading quantum corrections throughout the computation of the T^6 coefficient of the Taylor expansion of sigma(T). Furthermore, this coefficient results to be related to the universal ratio T_c/\sqrt{sigma_0}.