Phases of Wilson Lines in Conformal Field Theories

TL;DR

This paper investigates the behavior and screening of Wilson lines in conformal gauge theories across various dimensions, revealing universal screening phenomena, fixed-point mergers, and the role of charged matter fields in the low-energy limit.

Contribution

It provides a comprehensive analysis of Wilson line screening, including the identification of conformal Wilson lines, screening mechanisms, and the effects of fixed-point mergers in different gauge theories.

Findings

Wilson lines can become marginal leading to RG flows.

Large representations lead to screening by charged matter fields.

Screening involves fixed-point mergers and dimensional transmutation.

Abstract

We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in 2+1 and 3+1 dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to interesting renormalization group flows and for sufficiently large representations to complete or partial screening by charged fields. This result is universal: in large enough representations, Wilson lines are screened by the charged matter fields. We observe that the onset of the screening instability is associated with fixed-point mergers. We study this phenomenon in a variety of applications. In some cases, the screening of the Wilson lines takes place by dimensional transmutation and the generation of an exponentially large scale. We identify the space of infrared conformal Wilson lines in weakly coupled gauge theories in 3+1 dimensions and determine the screening cloud due to bosons or fermions. We also study QED in 2+1 dimensions in the large $N_f$ limit and identify the nontrivial conformal Wilson lines. We briefly discuss 't Hooft lines in 3+1-dimensional gauge theories and find that they are screened in weakly coupled gauge theories with simply connected gauge groups. In non-Abelian gauge theories with S-duality, this together with our analysis of the Wilson lines gives a compelling picture for the screening of the line operators as a function of the coupling.