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

TL;DR

This study investigates the effective string theory in the gauge dual of 3D percolation, revealing that while lower-order temperature terms match Nambu-Goto predictions, the higher-order term is unique to this universality class.

Contribution

It provides the first detailed calculation of the string tension up to order T^6 in the gauge dual of 3D percolation, highlighting deviations from Nambu-Goto at higher orders.

Findings

T^2 and T^4 coefficients match Nambu-Goto predictions.

The T^6 term differs significantly, indicating universality class-specific behavior.

Finite temperature string tension data collapse onto a single scaling function.

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.