CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
The $a$-theorem and the Asymptotics of 4D Quantum Field Theory
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that if the IR (UV) asymptotics is described by perturbation theory, all beta functions must vanish faster than $(1/|\ln\mu|)^{1/2}$ as $\mu \to 0$ ($\mu \to \infty$). This implies that the only possible asymptotics within perturbation theory is conformal field theory. In particular, it rules out perturbative theories with scale but not conformal invariance, which are equivalent to theories with renormalization group pseudocycles. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise.
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Decoherence in scale-invariant environments is uniquely equivalent to an unparticle bath characterized by scaling dimension d_U, which fixes all exponents via consistency relations and predicts a coherence-protection transition at d_U = 5/2.
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
Scale-invariant open quantum systems are universally described by unparticle baths with scaling dimension d_U, producing non-Markovian kernels, a fractional Caldeira-Leggett master equation, and phase transitions at d_U = 3/2, 2, and 5/2.
Derives lower bound on collective mean free path ℓ = √(τ D) in Drude-Kadanoff-Martin model from Green's function bounds, implying Mott-Ioffe-Regel limit for lattice models.
citing papers explorer
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Moduli Spaces in CFT: Large Charge Operators
CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
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Universal Description of Decoherence in Scale-Invariant Environments
Decoherence in scale-invariant environments is uniquely equivalent to an unparticle bath characterized by scaling dimension d_U, which fixes all exponents via consistency relations and predicts a coherence-protection transition at d_U = 5/2.
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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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Scale-Invariant Open Quantum Systems
Scale-invariant open quantum systems are universally described by unparticle baths with scaling dimension d_U, producing non-Markovian kernels, a fractional Caldeira-Leggett master equation, and phase transitions at d_U = 3/2, 2, and 5/2.
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Bootstrapping transport in the Drude-Kadanoff-Martin model
Derives lower bound on collective mean free path ℓ = √(τ D) in Drude-Kadanoff-Martin model from Green's function bounds, implying Mott-Ioffe-Regel limit for lattice models.
- Matching $A$ with $F$ in long-range QFTs