Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
Long-range vector models at large N
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Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
Long-range φ⁴ theories have RG beta functions that satisfy a gradient flow with A matching the sphere free energy F̃ at leading nontrivial order.
citing papers explorer
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Protected operators in non-local defect CFTs from AdS
Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
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Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
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Matching $A$ with $F$ in long-range QFTs
Long-range φ⁴ theories have RG beta functions that satisfy a gradient flow with A matching the sphere free energy F̃ at leading nontrivial order.