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arXiv:2508.14963 · Journal of High Energy Physics

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

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

Published Apr 9, 2026• 2 citations
arXivHTMLPDF

Abstract

A bstract 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- $$ \frac{1}{2} $$ 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.

DOI
10.1007/jhep04(2026)071

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A bstract 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- 12\frac{1}{2}21​ 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.
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We use the fuzzy-sphere approach to study the Bose-Kondo impurity problem, namely a spin-SSS impurity coupled to the (2+1)(2+1)(2+1)-dimensional O(3)O(3)O(3) Wilson-Fisher CFT (Heisenberg universality class). We demonstrate that for S=1/2,1,3/2S=1/2,1,3/2S=1/2,1,3/2 the impurity flows to a distinct stable interacting conformal defect for each SSS. Using large-scale exact diagonalization and density-matrix renormalization group methods, we observe integer-spaced defect spectrum consistent with defect conformal symmetry and compute several low-lying defect primary operators as well as the RG monotonic ggg-function. Our findings show that despite sharing the same symmetry and anomaly, Bose-Kondo impurities flow to distinct stable infrared conformal fixed points, which we refer to as \emph{fortuitous universality}. We expect this fortuitous universality to persist for all SSS, extending to S→∞S\rightarrow\inftyS→∞, with each spin-SSS impurity flowing to its own stable infrared conformal fixed point.
A bstract In this work, we study the realization of non-invertible duality symmetries along the toroidal branch of the c = 2 conformal manifold. A systematic procedure to construct symmetry defects is implemented to show that all Rational Conformal Field Theories along this branch enjoy duality symmetries. Furthermore, we delve into an in-depth analysis of two representative cases of multicritical theories, where the toroidal branch meets various orbifold branches. For these particular examples, the categorical data and the defect Hilbert spaces associated with the duality symmetries are obtained by resorting to modular covariance. Finally, we study the interplay between these novel symmetries and the various exactly marginal and relevant deformations, including some representative examples of Renormalization Group flows where the infrared is constrained by the non-invertible symmetries and their anomalies.
A bstract Topological defect lines (TDLs) in two-dimensional conformal field theories (CFTs) are standard examples of generalized symmetries in quantum field theory. Integrable lattice incarnations of these TDLs, such as those provided by spin/anyonic chains, provide a crucial playground to investigate their properties, both analytically and numerically. Here, a family of parameter-dependent integrable lattice models is presented, which realize different TDLs in a given CFT as the parameter is varied. These models are based on the general quantum-inverse scattering construction, and involve inhomogeneities of the spectral parameter. Both defect hamiltonians and (defect) line operators are obtained in closed form. By varying the inhomogeneities, renormalization group flows between different TDLs (such as the Verlinde lines associated with the Virasoro primaries (1 , s ) and ( r, 1) in diagonal minimal CFTs) are then studied using different aspects of the Bethe-ansatz as well as ab-initio numerical techniques. Relationships with the anisotropic Kondo model as well as its non-Hermitian version are briefly discussed.
A bstract We use the intrinsic one-form and two-form global symmetries of (3+1) d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1) d . We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1) d for SU(2) gauge theory with two adjoint Weyl fermions.
Abstract In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations , cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.