Fractionalization of flux tubes in 3d and screening by emergent electric charges in 2d

TL;DR

This paper explores how flux tubes fractionalize and how emergent electric charges screen Wilson loops in 3D theories with $ ext{Z}_n$ magnetic symmetry, revealing fractional electric charges at domain junctions.

Contribution

It demonstrates the fractionalization of confining strings and the emergence of fractional electric charges in a class of 3D theories with $ ext{Z}_n$ symmetry, using twisted compactification techniques.

Findings

Large Wilson loops are screened for even/odd n.

Flux tubes split into n strings with 1/n electric flux.

Emergent fractional electric charges appear at domain junctions.

Abstract

We consider a class of 3d theories with a $\mathbb Z_n$ magnetic symmetry in which confinement is generated by charge $n$ clusters of monopoles. Such theories naturally arise in quantum antiferromagnets in 2+1, QCD-like theories on $\mathbb R^3 \times S^1$, and $U(1)$ lattice theory with restricted monopole sums. A confining string fractionates into $n$ strings which each carry $1/n$ electric flux. We construct a twisted compactification (equivalently periodic compactification with a topological defect insertion) on $\mathbb R^2 \times S^1$ that preserves the vacuum structure. Despite the absence of electric degrees of freedom in the microscopic Lagrangian, we show that large Wilson loops are completely/partially screened for even/odd $n$, even when the compactification scale is much larger than the Debye length. We show the emergence of fractional electric charges $(\pm 2/n)$ at the junctions of the domain lines and topological defects. We end with some remarks on screening vs. confinement.