DOI: 10.1007/jhep10(2026)208 ISSN: 1029-8479

Quark anti-quark fusion and walking RG flows

Filipp Chernikov, Nikolay Gromov, Amit Sever
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A
bstract

We study the fusion of two conjugate conformal line defects on the sphere. We first derive the spectrum at small separation in the planar ladder model, and then obtain an exact finite-coupling description of the fusion of conjugate 1/2-BPS Wilson lines in planar

$$ \mathcal{N} $$ N
= 4 SYM using the Quantum Spectral Curve. These results reveal that the 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, ℝ ) Casimir continues to commute with the Hamiltonian below that scale. This organizes the spectrum into conformal families and fixes a universal, scheme-independent density of states. We test our results against perturbation theory and semiclassical string theory.

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