Ising string beyond Nambu-Goto

TL;DR

This paper investigates higher-order corrections to the Effective String Theory for confinement, focusing on the three-dimensional gauge Ising model, and provides numerical estimates of these corrections beyond the Nambu-Goto approximation.

Contribution

It numerically evaluates the first two higher-order corrections in EST beyond Nambu-Goto for the 3D gauge Ising model, advancing understanding of confinement mechanisms.

Findings

First correction is negative: γ₃ = -0.00048(4).

Result is similar to measurements in 3D SU(2) Yang-Mills.

Compatible with bootstrap bound γ₃ ≥ -1/768.

Abstract

A major result of the Effective String Theory (EST) description of confinement is the so called "low energy universality," which states that the first few terms of the large distance expansion of any EST are universal and coincide with those of the Nambu-Goto action. Going beyond this approximation is one of the most interesting open problems in the EST. In the higher order terms beyond Nambu-Goto several important pieces of physical information are encoded, which could improve our understanding of the physical mechanisms behind confinement and of the physical degrees of freedoms which originate the EST. In this paper we evaluate numerically the first two of these corrections in the case of the three dimensional gauge Ising model. The first of them turns out to be negative: $\gamma_3=-0.00048(4)$, similar (but not equal) to the one recently measured in the $SU(2)$ Yang Mills theory in three dimensions and compatible with the bootstrap bound $\gamma_3 \geq -\frac{1}{768}$.