Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions

TL;DR

This paper investigates the effective string description of SU(2) Yang-Mills theory in three dimensions, combining lattice simulations and analytical methods to bound corrections beyond the Nambu-Goto model, with implications for the Axionic String Ansatz.

Contribution

It provides the first tight quantitative bounds on corrections to the effective string action in three-dimensional SU(2) Yang-Mills theory, integrating multiple analytical and numerical approaches.

Findings

Corrections are compatible with bootstrap predictions.

Corrections do not support the Axionic String Ansatz.

High-precision lattice data constrains effective string models.

Abstract

We present a study of the effective string that describes the infrared dynamics of SU(2) Yang-Mills theory in three dimensions. By combining high-precision lattice simulation results for Polyakov-loop correlators at finite temperatures close to (and less than) the deconfinement one with the analytical constraints from renormalization-group arguments, from the exact integrability of the two-dimensional Ising model that describes the universality class of the critical point of the theory, from conformal perturbation theory, and from Lorentz invariance, we derive tight quantitative bounds on the corrections to the effective string action beyond the Nambu-Goto approximation. We show that these corrections are compatible with the predictions derived from a bootstrap analysis of the effective string theory, and have a value which does not allow to prove the Axionic String Ansatz for this model