Anomalous dimensions of leading twist conformal operators

Abstract

We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-point functions of descendants and of their primaries determines the anomalous dimension, allowing us to gain an order of perturbation theory. We demonstrate the efficiency of the formalism on the lowest-order analysis of anomalous dimensions and mixing matrices which is required for two-loop calculations of the former. We compare these results to another method based on anomalous conformal Ward identities and constraints from the conformal algebra. It also permits to gain a perturbative order in computations of mixing matrices. We show the complete equivalence of both approaches.

21 pages, 4 figures; references added

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Cited by in corpus (18)

• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Notes on Spinning Operators in Fermionic CFT
• TASI Lectures on the Higher Spin - CFT duality
• Duality between Wilson loops and gluon amplitudes
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• Reciprocity of gauge operators in N=4 SYM
• Correlation functions of local composite operators from generalized unitarity
• On (Un)Broken Higher-Spin Symmetry in Vector Models
• The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector
• Analytic bootstrap for magnetic impurities
• On structure constants with two spinning twist-two operators
• Broken current anomalous dimensions, conformal manifolds and RG flows
• Conformal constraints for anomalous dimensions of leading twist operators
• QCD-like properties for anomalous dimensions in N=4 SYM
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Superfield twist-$2$ operators in $\mathcal{N}=1$ SCFTs and their renormalization-group improved generating functional in $\mathcal{N}=1$ SYM theory