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<p>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 <i>g</i>-theorem.</p><p>As an example, we prove that the spin-<InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( \frac{1}{2} \)</EquationSource> </InlineEquation> impurities in the 2+1d critical <i>O</i>(2) and <i>O</i>(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 <i>s</i>. We also argue that, under particle/vortex duality, the Halon impurity is exchanged with the <i>π</i>-flux vortex line leading to <i>spin-flux duality</i>, a proposal which we test with a detailed matching of symmetries, anomalies, and phases.</p><p>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.</p>

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Defect anomalies, a spin-flux duality, and Boson-Kondo problems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月9日

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  • Zohar Komargodski,
  • Fedor K. Popov,
  • Brandon C. Rayhaun

摘要

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 \( \frac{1}{2} \) 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 π-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.