Anomalous dimensions of higher spin currents in large N CFTs

Abstract

We examine anomalous dimensions of higher spin currents in the critical O(N) scalar model and the Gross-Neveu model in arbitrary d dimensions. These two models are proposed to be dual to the type A and type B Vasiliev theories, respectively. We reproduce the known results on the anomalous dimensions to the leading order in 1/N by using conformal perturbation theory. This work can be regarded as an extension of previous work on the critical O(N) scalars in 3 dimensions, where it was shown that the bulk computation for the masses of higher spin fields on AdS_4 can be mapped to the boundary one in conformal perturbation theory. The anomalous dimensions of the both theories agree with each other up to an overall factor depending only on d, and we discuss the coincidence for d=3 by utilizing N=2 supersymmetry.

arXiv comment36 pages, 5 figures, minor changes, references added, published version

References in corpus (35)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• AdS Dual of the Critical O(N) Vector Model
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Fractional M2-branes
• Quantum Field Theory in the Large N Limit: a review
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theories: Star-Product and AdS Space
• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Tensionless Strings and the Weak Gravity Conjecture
• Higher Spins & Strings
• Holography of the N=1 Higher-Spin Theory on AdS4
• Large N=4 Holography
• Compensating strong coupling with large charge
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• On Higher Spin Gauge Theory and the Critical O(N) Model
• 3-D Interacting CFTs and Generalized Higgs Phenomenon in Higher Spin Theories on AdS
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• Higher-spin current multiplets in operator-product expansions
• Higher spin AdS_3 holography with extended supersymmetry
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion
• On $C_J$ and $C_T$ in the Gross-Neveu and $O(N)$ Models
• More on analytic bootstrap for O(N) models
• On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
• On Calculation of 1/n Expansions of Critical Exponents in the Gross-Neveu Model with the Conformal Technique
• Massless and Massive Higher Spins from Anti-de Sitter Space Waveguide
• Rainbow Vacua of Colored Higher Spin Gravity in Three Dimensions
• Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model
• Higgs phenomenon for higher spin fields on AdS_3
• Marginal deformations and the Higgs phenomenon in higher spin AdS_3 holography
• The masses of higher spin fields on AdS_4 and conformal perturbation theory

Cited by in corpus (7)

• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Spinning AdS Loop Diagrams: Two Point Functions
• Notes on Spinning Operators in Fermionic CFT
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• Fermions in Geodesic Witten Diagrams
• Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry