Defect Anomalies, a Spin-Flux Duality, and Boson-Kondo Problems

TL;DR

This paper explores the role of anomalies in determining the infrared phases of line defects in 2+1d quantum field theories, revealing dualities and proposing lattice models for experimental tests.

Contribution

It demonstrates how anomalies influence defect phases, proves IR conformal behavior for certain impurities, and introduces a spin-flux duality with lattice Hamiltonians for validation.

Findings

Infrared phases are anomaly-dependent.

Spin-1/2 impurities flow to conformal line operators.

Spin-flux duality relates impurities and vortices.

Abstract

We show that the infrared phases of certain line defects in 2+1d quantum field theories are determined by anomalies, including anomalies in the space of defect coupling constants, together with a symmetry-refined corollary of the $g$-theorem. As an example, we prove that the spin-$1/2$ impurities in the 2+1d critical $O(2)$ and $O(3)$ models (known respectively as the Halon and Boson-Kondo defects) flow to non-trivial conformal line operators in the IR, and we supply evidence that the same extends to all spin $s$. We also argue that, under particle/vortex duality, the Halon impurity is exchanged with the $\pi$-flux vortex line leading to spin-flux duality, a proposal which we test with a detailed matching of symmetries, anomalies, and phases. Finally, we write down quantum lattice Hamiltonians which can be used to test our predictions, and give an argument on the lattice in favor of spin-flux duality.