Phases of Wilson Lines: Conformality and Screening

TL;DR

This paper explores the complex behavior of Wilson lines in various gauge theories, revealing multiple fixed points, screening phenomena, and their implications for condensed matter and duality concepts.

Contribution

It provides a comprehensive analysis of Wilson line dynamics across different dimensions and theories, including new insights into screening and fixed points.

Findings

Wilson lines can be fully or partially screened depending on charges.

Multiple defect fixed points with RG flows are identified.

Screening clouds define emergent length scales.

Abstract

We study the rich dynamics resulting from introducing static charged particles (Wilson lines) in 2+1 and 3+1 dimensional gauge theories. Depending on the charges of the external particles, there may be multiple defect fixed points with interesting renormalization group flows connecting them, or an exponentially large screening cloud can develop (defining a new emergent length scale), screening the bare charge entirely or partially. We investigate several examples where the dynamics can be solved in various weak coupling or double scaling limits. Sometimes even the elementary Wilson lines, corresponding to the lowest nontrivial charge, are screened. We consider Wilson lines in 3+1 dimensional gauge theories including massless scalar and fermionic QED$_4$, and also in the ${\mathcal N}=4$ supersymmetric Yang-Mills theory. We also consider Wilson lines in 2+1 dimensional conformal gauge theories such as QED$_3$ with bosons or fermions, Chern-Simons-Matter theories, and the effective theory of graphene. Our results in 2+1 dimensions have potential implications for graphene, second-order superconducting phase transitions, etc. Finally, we comment on magnetic line operators in 3+1 dimensions ('t Hooft lines) and argue that our results for the infrared dynamics of electric and magnetic lines are consistent with non-Abelian electric-magnetic duality.