Fusion of conjugate line defects exhibits walking RG at criticality with SL(2,R) Casimir fixing scheme-independent spectrum density, derived exactly in N=4 SYM via Quantum Spectral Curve.
A Model Study of Discrete Scale Invariance and Long-Range Interactions
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abstract
We investigate the modification of discrete scale invariance in the bound state spectrum by long-range interactions. This problem is relevant for effective field theory descriptions of nuclear cluster states and manifestations of the Efimov effect in nuclei. As a model system, we choose a one dimensional inverse square potential supplemented with a long-range Coulomb interaction. We study the renormalization and bound-state spectrum of the system as a function of the Coulomb interaction strength. Our results indicate, that the counterterm required to renormalize the inverse square potential alone is sufficient to renormalize the full problem. However, the breaking of the discrete scale invariance through the Coulomb interaction leads to a modified bound state spectrum. The shallow bound states are strongly influenced by the Coulomb interaction while the deep bound states are dominated by the inverse square potential.
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2026 2verdicts
UNVERDICTED 2representative citing papers
A DNN solves the symmetrized spectator form of the subtracted Faddeev equations for three identical bosons, reproducing Efimov binding scales at unitarity to within 0.022% and tracing bound-state branches versus inverse scattering length.
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Quark Anti-Quark Fusion and Walking RG Flows
Fusion of conjugate line defects exhibits walking RG at criticality with SL(2,R) Casimir fixing scheme-independent spectrum density, derived exactly in N=4 SYM via Quantum Spectral Curve.
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Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit
A DNN solves the symmetrized spectator form of the subtracted Faddeev equations for three identical bosons, reproducing Efimov binding scales at unitarity to within 0.022% and tracing bound-state branches versus inverse scattering length.