The scheme-independent 3-sphere free energy decreases at O(g^2) under relevant deformations of a 3D CFT but is not monotone along the full RG flow of the free massive scalar on S^3.
Nakayama, Scale invariance vs conformal invariance, Phys
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this review article, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant quantum field theories in $d=2$ dimension necessarily possess the enhanced conformal symmetry. The use of the conformal symmetry is well appreciated in the literature, but the fact that all the scale invariant phenomena in $d=2$ dimension enjoy the conformal property relies on the deep structure of the renormalization group. The outstanding question is whether this feature is specific to $d=2$ dimension or it holds in higher dimensions, too. As of January 2014, our consensus is that there is no known example of scale invariant but non-conformal field theories in $d=4$ dimension under the assumptions of (1) unitarity, (2) Poincar\'e invariance (causality), (3) discrete spectrum in scaling dimension, (4) existence of scale current and (5) unbroken scale invariance in the vacuum. We have a perturbative proof of the enhancement of conformal invariance from scale invariance based on the higher dimensional analogue of Zamolodchikov's $c$-theorem, but the non-perturbative proof is yet to come. As a reference we have tried to collect as many interesting examples of scale invariance in relativistic quantum field theories as possible in this article. We give a complementary holographic argument based on the energy-condition of the gravitational system and the space-time diffeomorphism in order to support the claim of the symmetry enhancement. We believe that the possible enhancement of conformal invariance from scale invariance reveals the sublime nature of the renormalization group and space-time with holography.
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A PT-symmetric non-Hermitian free-fermion field theory realizes logarithmic conformal field theory with central charge c=-2 via a biorthogonal Virasoro algebra construction.
The Paneitz operator in 4D belongs to extended mimetic gravity and is constrained by gravitational wave propagation speed.
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.
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.
An 't Hooft anomaly at general imaginary baryon chemical potential constrains the QCD chiral transition to three minimal CFT scenarios, with the favored one for N_f >= 3 featuring a conformal manifold of theta_B-dependent universality classes with an exactly marginal operator tied to baryon density.
Radiative electroweak symmetry breaking with a logarithmic potential yields analytical vacuum solutions, four thermal history patterns, and supercooled FOPT gravitational waves whose signals combined with collider data can probe conformal scales to 10^5-10^8 GeV.
Computes the beta function for the inverse square potential in conformal quantum mechanics to arbitrary perturbative and non-perturbative orders in both bound state and scattering sectors.
citing papers explorer
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The scheme independent 3-sphere free energy is not a monotone F-function
The scheme-independent 3-sphere free energy decreases at O(g^2) under relevant deformations of a 3D CFT but is not monotone along the full RG flow of the free massive scalar on S^3.
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Non-Hermitian free-fermion critical systems and logarithmic conformal field theory
A PT-symmetric non-Hermitian free-fermion field theory realizes logarithmic conformal field theory with central charge c=-2 via a biorthogonal Virasoro algebra construction.
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Gravitational wave constraints on the Paneitz operator
The Paneitz operator in 4D belongs to extended mimetic gravity and is constrained by gravitational wave propagation speed.
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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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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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Does hot QCD have a conformal manifold in the chiral limit?
An 't Hooft anomaly at general imaginary baryon chemical potential constrains the QCD chiral transition to three minimal CFT scenarios, with the favored one for N_f >= 3 featuring a conformal manifold of theta_B-dependent universality classes with an exactly marginal operator tied to baryon density.
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Probing radiative electroweak symmetry breaking with colliders and gravitational waves
Radiative electroweak symmetry breaking with a logarithmic potential yields analytical vacuum solutions, four thermal history patterns, and supercooled FOPT gravitational waves whose signals combined with collider data can probe conformal scales to 10^5-10^8 GeV.
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Renormalization and Non-perturbative Dynamics in Conformal Quantum Mechanics
Computes the beta function for the inverse square potential in conformal quantum mechanics to arbitrary perturbative and non-perturbative orders in both bound state and scattering sectors.