Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
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abstract
We consider the continuation of free and interacting scalar field theory to non-integer spacetime dimension d. We find that the correlation functions in these theories are necessarily incompatible with unitarity (or with reflection positivity in Euclidean signature). In particular, the theories contain negative norm states unless d is a positive integer. These negative norm states can be obtained via the OPE from simple positive norm operators, and are therefore an integral part of the theory. At the Wilson-Fisher fixed point the non-unitarity leads to the existence of complex anomalous dimensions. We demonstrate that they appear already at leading order in the epsilon expansion.
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A prototype successfully upgrades low-order extremal flow solutions to high numerical order for gap maximization in a simple spinning modular bootstrap test case.
SAR regularizes φ⁴ and Yukawa theories at NLO by analytically continuing the power of the kinetic operator in the action.
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.
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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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Upgrading Extremal Flows in the Space of Derivatives
A prototype successfully upgrades low-order extremal flow solutions to high numerical order for gap maximization in a simple spinning modular bootstrap test case.
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Systematic Analytic Regularization in $\varphi^4$ and Yukawa Theories
SAR regularizes φ⁴ and Yukawa theories at NLO by analytically continuing the power of the kinetic operator in the action.
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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.