String effects in Yang-Mills theory

TL;DR

This paper investigates the properties of confining strings in Yang-Mills theory through numerical simulations, confirming theoretical predictions about flux tube broadening and analyzing the behavior of stable and unstable strings in various representations.

Contribution

It provides quantitative verification of effective string theory predictions and explores the behavior of k-strings and unstable strings in (2+1)-d Yang-Mills theory.

Findings

Flux tube thickness increases with source separation.

Logarithmic broadening observed at zero temperature.

Linear broadening of flux tube at finite temperature.

Abstract

We study some features of the confining string connecting a quark-anti-quark pair in Yang-Mills theory. Monte Carlo investigations of the flux tube between two static quarks in the fundamental representation show that its thickness increases with the separation of the sources. The collected numerical data in (2+1)-d SU(2) Yang-Mills theory are in very good quantitative agreement with the next-to-leading order formula derived from the systematic low-energy effective theory of the confining string. At zero temperature, we observe the predicted logarithmic broadening. At finite and low temperature, the flux tube thickness is expected to broaden linearly. We also verify that prediction, finding an excellent agreement with the analytic expression. No adjustable parameter has been used to fit the numerical data. Then we investigate the confining strings connecting color sources in larger representations of the gauge group. Concerning stable strings -- the k-strings -- we study the Luscher term of the fundamental string and of the 2-string in (2+1)-d SU(4) Yang-Mills theory. We find that, at large separation between the two static sources, the coefficient of the Luscher term of the 2-string appraoches the value -pi/24. However, at intermediate distances, there are relevant deviations. This result may suggest that, for SU(N) at large N, a different intermediate string regime could set in. For unstable strings, in (2+1)-d SU(2) Yang-Mills theory we investigate the decay between two different string states and the multiple decays of the confining string connecting color sources in large representations. The multiple decays result from the progressive partial screening of the color sources.