Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories

Abstract

In the free ${\square }^k$ scalar conformal field theory, there exist conserved and partially-conserved higher-spin currents. We study their anomalous dimensions associated with ${\varphi }^{2n}$ interaction in the $\epsilon$ expansion. We derive general formulae for the leading corrections from the conformal multiplet recombination, and verify their consistency with crossing symmetry using the Lorentzian inversion formula. The results are further extended to the O($N$) models.

arXiv commentv3: 34 pages, 4 figures, discussion improved, references added, typos corrected; v2: discussion about the N dependence of Chew-Frautschi plot added, Fig.3 and Fig. 4 added, typos corrected, minor improvements, notation simplified, references updated

References in corpus (87)

• Gauge Theory Correlators from Non-Critical String Theory
• AdS Dual of the Critical O(N) Vector Model
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Conformal Partial Waves and the Operator Product Expansion
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Writing CFT correlation functions as AdS scattering amplitudes
• Logarithmic Operators in Conformal Field Theory
• Precision Islands in the Ising and $O(N)$ Models
• The Analytic Bootstrap and AdS Superhorizon Locality
• Spinning Conformal Correlators
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• Partial Masslessness of Higher Spins in (A)dS
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Unitarity and the Holographic S-Matrix
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• More constraining conformal bootstrap
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• On the cubic interactions of massive and partially-massless higher spins in (A)dS
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Generating functions of (partially-)massless higher-spin cubic interactions
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• The critical O(N) CFT: Methods and conformal data
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Notes on Spinning Operators in Fermionic CFT
• Conformal Operators for Partially Massless States
• Free box^k Scalar Conformal Field Theory
• CFT in AdS and boundary RG flows
• Generalized Wilson-Fisher critical points from the conformal OPE
• Partially-massless higher-spin algebras and their finite-dimensional truncations
• More on La Grande Bouffe: towards higher spin symmetry breaking in AdS
• The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
• Detectors in weakly-coupled field theories
• $C_T$ for Non-unitary CFTs in Higher Dimensions
• Radial Dimensional Reduction: (Anti) de Sitter Theories from Flat
• Renormalization Theory for Interacting Crumpled Manifolds
• Partially Massless Higher-Spin Theory
• $\epsilon$-Expansion in the Gross-Neveu Model from Conformal Field Theory
• Leading CFT constraints on multi-critical models in d>2
• Classical equation of motion and Anomalous dimensions at leading order
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Solving Conformal Field Theories with Artificial Intelligence
• Fermions in AdS and Gross-Neveu BCFT
• Critical O(N) model to order ${\epsilon }^4$ from analytic bootstrap
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• Aspects of CFTs on Real Projective Space
• On Analytic Bootstrap for Interface and Boundary CFT
• $\epsilon$-Expansion in the Gross-Neveu CFT
• Coupled minimal models revisited
• Uniformizing higher-spin equations
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Higher Symmetries of the Laplacian via Quantization
• Null bootstrap for non-Hermitian Hamiltonians
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• Higher spin currents in the critical $O(N)$ vector model at $1/N^2$
• Leading order CFT analysis of multi-scalar theories in d>2
• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• The $\epsilon$-expansion of the codimension two twist defect from conformal field theory
• Spectrum of anomalous dimensions in hypercubic theories
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Taming Dyson-Schwinger equations with null states
• Higher dimensional higher derivative ${\varphi }^4$ theory
• Three ways to solve critical ${\varphi }^4$ theory on $4-\epsilon$ dimensional real projective space: perturbation, bootstrap, and Schwinger-Dyson equation
• Anomalous dimensions of spinning operators from conformal symmetry
• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Multi-critical ${\square }^k$ scalar theories: A perturbative RG approach with $\epsilon$-expansion
• Ising model close to $d=2$
• Interacting conformal scalar in a wedge
• Multi-critical multi-field models: a CFT approach to the leading order
• Conformal Bootstrap Deformations
• The O(N)-flavoured replica twist defect
• Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
• Factorized lightcone expansion of conformal blocks

Cited by in corpus (6)

• Principle of minimal singularity for Green's functions
• The tricritical Ising CFT and conformal bootstrap
• Coupled minimal models revisited II: Constraints from permutation symmetry
• ${\varphi }^n$ trajectory bootstrap
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations