Geometric Aspects of Confining Strings

TL;DR

This paper explores the geometric properties of confining strings in 4D gauge theories, revealing their duality with gauge fields and describing phase transitions from smooth to fractal world-sheets.

Contribution

It demonstrates the duality between confining strings and gauge fields and characterizes the geometric transition of string world-sheets across different coupling regimes.

Findings

Confining strings are dual to gauge fields, especially in the strong coupling regime.

At critical points, world-sheets become fractal with diverging intrinsic distances.

Phase transition marks the loss of smooth string surfaces, leading to fractal geometries.

Abstract

Confining strings in 4D are effective, thick strings describing the confinement phase of compact U(1) and, possibly, also non-Abelian gauge fields. We show that these strings are dual to the gauge fields, inasmuch as their perturbative regime corresponds to the strong coupling (large e) regime of the gauge theory. In this regime they describe smooth surfaces with long-range correlations and Hausdorff dimension two. For lower couplings e and monopole fugacities z, a phase transition takes place, beyond which the smooth string picture is lost. On the critical line intrinsic distances on the surface diverge and correlators vanish, indicating that world-sheets become fractal.