The confining string beyond the free-string approximation in the gauge dual of percolation

TL;DR

The paper investigates the finite-temperature behavior of the confining string in the gauge dual of three-dimensional random percolation, testing the IR effective string description beyond the free-string approximation. By computing Polyakov-loop correlators across multiple percolation realizations, lattice types, and sizes, the authors extract a universal scaling function for the temperature-dependent string tension and determine the first few terms in its expansion. They find that the $T^2$ and $T^4$ terms agree with the Nambu-Goto predictions, while the $T^6$ term deviates, with the deviation robust across the studied universality class. This establishes a universal, non-Nambu–Goto feature of the confining string in this gauge dual and demonstrates a precise method to resolve high-order string corrections in simple gauge models. The work also provides a continuum-extrapolated value for $T_c/\,$ and highlights the role of universality in determining effective string dynamics in confining gauge theories.

Abstract

We simulate five different systems belonging to the universality class of the gauge dual of three-dimensional random percolation to study the underlying effective string theory at finite temperature. All the data for the finite temperature string tension, when expressed by means of adimensional variables, are nicely described by a unique scaling function. We calculate the first few terms of the string tension up to order $T^6$ and compare to different theoretical predictions. We obtain unambiguous evidence that the coefficients of $T^2$ and $T^4$ terms coincide with those of the Nambu-Goto string, as expected, while the $T^6$ term strongly differs and is characteristic of the universality class of this specific gauge theory.