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arXiv · 2607.01328

Quark Anti-Quark Fusion and Walking RG Flows

Filipp Chernikov·Nikolay Gromov·Amit Sever
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Abstract

We study the fusion of two conjugate conformal line defects on the sphere. At small separation, their spectrum is governed by a universal Fusion Master Equation. Below a critical coupling, the fused defect has two conformal fixed points; at criticality, they collide and move into the complex plane, producing walking RG behaviour. Although individual energy levels then drift with the UV scale and are scheme dependent, the $SL(2,\mathbb{R})$ Casimir continues to commute with the Hamiltonian below that scale. This organises the spectrum into conformal families and fixes a universal, scheme-independent density of states. We derive this structure in the planar ladder model and obtain an exact finite-coupling description of conjugate $1/2$-BPS Wilson-line fusion in planar ${\cal N}=4$ SYM using the Quantum Spectral Curve. We test our results against perturbation theory and semiclassical string theory.

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Filipp Chernikov, Nikolay Gromov, Amit Sever. 2026-07-01. Quark Anti-Quark Fusion and Walking RG Flows. https://arxiv.org/abs/2607.01328

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