The Uses of Conformal Symmetry in QCD

Abstract

The Lagrangian of Quantum Chromodynamics is invariant under conformal transformations. Although this symmetry is broken by quantum corrections, it has important consequences for strong interactions at short distances and provides one with powerful tools in practical calculations. In this review we give a short exposition of the relevant ideas, techniques and applications of conformal symmetry to various problems of interest.

arXiv comment110 pages, invited review for "Prog. Part. Nucl. Phys"

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• Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD
• A semi-classical limit of the gauge/string correspondence
• Renormalons
• Scaling Limit of Deeply Virtual Compton Scattering
• Measurements of the Meson-Photon Transition Form Factors of Light Pseudoscalar Mesons at Large Momentum Transfer
• Higher Twist Distribution Amplitudes of Vector Mesons in QCD: Formalism and Twist Three Distributions
• High energy QCD as a completely integrable model
• Theoretical Update of Pseudoscalar Meson Distribution Amplitudes of Higher Twist: The Nonsinglet Case
• Structure functions for large $x$ and renormalization of Wilson loops
• The $\rho$ Meson Light-Cone Distribution Amplitudes of Leading Twist Revisited
• Baryon Distribution Amplitudes in QCD
• Two-loop effective potential for a general renormalizable theory and softly broken supersymmetry
• Higher Twist Distribution Amplitudes of Vector Mesons in QCD: Twist-4 Distributions and Meson Mass Corrections
• Probing partonic structure in gamma* gamma -> pi pi near threshold
• One-Loop Corrections and All Order Factorization In Deeply Virtual Compton Scattering
• Integrability of three-particle evolution equations in QCD
• Photon Distribution Amplitudes in QCD
• A New Odderon Solution in Perturbative QCD
• Commensurate Scale Relations in Quantum Chromodynamics
• Higher Twist Distribution Amplitudes of the Nucleon in QCD
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Broken conformal invariance and spectrum of anomalous dimensions in QCD
• Renormalization of twist-three operators and integrable lattice models
• Predictions from conformal algebra for the deeply virtual Compton scattering
• Solution of the Odderon Problem
• Integrability and WKB solution of twist-three evolution equations
• The Generalized Crewther Relation in QCD and its Experimental Consequences
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Evolution kernels of skewed parton distributions: method and two-loop results
• The Evolution of the Pion Distribution Amplitude in Next-to-Leading Order
• NLO Corrections to Deeply-Virtual Compton Scattering
• Bethe Ansatz for QCD Pomeron,
• Next-to-next-to-leading order prediction for the photon-to-pion transition form factor
• Quasiclassical QCD Pomeron
• Off-forward gluonometry
• Q^2 Evolution of Chiral-Odd Twist-3 Distributions h_L(x, Q^2) and e(x, Q^2) in Large-N_c QCD
• Restricted conformal invariance in QCD and its predictive power for virtual two-photon processes
• Next-to-leading order evolution of twist-two conformal operators: The abelian case
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum
• Solution of the multi-reggeon compound state problem in multi-colour QCD
• Relating inclusive e+e- annihilation to electroproduction sum rules in Quantum Chromodynamics
• Evolution equation for the structure function g_2(x,Q^2)
• Solution of the odderon problem for arbitrary conformal weights
• The annihilation of virtual photons into pseudoscalar mesons
• Exact resolution of the Baxter equation for reggeized gluon interactions
• Reconstruction of non-forward evolution kernels
• Evolution of twist-three parton distributions in QCD beyond the large N_c limit
• Relating Physical Observables in QCD without Scale-Scheme Ambiguity
• Implications of N=1 supersymmetry for QCD conformal operators
• Resummation of target mass corrections in two-photon processes: twist-two sector
• Exclusive evolution kernels in two-loop order: parity even sector
• NLO evolution kernels for skewed transversity distributions
• Gluon contribution to the structure function g_2(x,Q^2)
• Fixing the renormalisation scheme in NNLO perturbative QCD using conformal limit arguments
• Superconformal constraints for QCD conformal anomalies
• Parton distribution functions from nonlocal light-cone operators with definite twist
• Noncompact Heisenberg spin magnets from high-energy QCD: III. Quasiclassical approach
• Scheme dependence of NLO corrections to exclusive processes
• Renormalon Model of Twist-4 Corrections to the Pion Distribution Amplitude
• WKB quantization of reggeon compound states in high-energy QCD
• Ultraviolet dominance of power corrections in QCD?

Cited by in corpus (245)

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• An Operator Product Expansion for Polygonal null Wilson Loops
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• Twist-3 Distribution Amplitudes of K* and phi Mesons
• From correlation functions to Wilson loops
• Anomalous dimensions of high-spin operators beyond the leading order
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• Integrability in QCD and beyond
• The Renormalization Scale-Setting Problem in QCD
• From correlation functions to scattering amplitudes
• Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond
• A scaling theory for the long-range to short-range crossover and an infrared duality
• On Integrability of Classical SuperStrings in AdS_5 x S^5
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• Light-Cone Distribution Amplitudes of Axial-vector Mesons
• Conformal Invariance in the Long-Range Ising Model
• Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons
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• On The Pomeron at Large 't Hooft Coupling
• Baryon Spectrum from Superconformal Quantum Mechanics and its Light-Front Holographic Embedding
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• Matching Quasi Generalized Parton Distributions in the RI/MOM scheme
• Light meson spectrum and classical symmetries of QCD
• Quantum integrability in (super) Yang-Mills theory on the light-cone
• Asymptotic behavior of meson transition form factors
• Baryon Operators of Higher Twist in QCD and Nucleon Distribution Amplitudes
• One-Loop QCD Spin Chain and its Spectrum
• Pion distribution amplitude from lattice-QCD
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks
• Distribution Amplitudes of the Lambda_b Baryon in QCD
• Two-parton Light-cone Distribution Amplitudes of Tensor Mesons
• Dimensional Reduction for Conformal Blocks
• Sum rules and dualities for generalized parton distributions: is there a holographic principle?
• Structure of large spin expansion of anomalous dimensions at strong coupling
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• Exact Correlation Functions in Conformal Fishnet Theory
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Improved Light-Cone Sum Rules for the Electromagnetic Form Factors of the Nucleon
• Solving 2D QCD with an adjoint fermion analytically
• Renormalization of Twist-Four Operators in QCD
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Spinning Gluons from the QCD Light-Ray OPE
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Kinematic power corrections in off-forward hard reactions
• Einstein gravity from ANEC correlators
• On Conformal Field Theories With Extremal a/c Values
• Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator
• Light Cone Sum Rules for gamma* N -> Delta Transition Form Factors
• $C_T$ for Non-unitary CFTs in Higher Dimensions
• Transverse momentum dependent operator expansion at next-to-leading power
• Distribution amplitudes of light-quark mesons from lattice QCD
• Towards a fitting procedure to deeply virtual meson production -- the next-to-leading order case --
• Quantum mechanics of null polygonal Wilson loops
• $B\to f_0(980)K$ Decays and Subleading Corrections
• Precision calculations of $B_{d,s}\to \pi ,K$ decay form factors in soft-collinear effective theory
• Evolution equations beyond one loop from conformal symmetry
• Model Independent Results for SU(3) Violation in Light-Cone Distribution Functions
• Two-loop evolution equation for the B-meson distribution amplitude
• Duality between Wilson loops and gluon amplitudes
• Integrability of two-loop dilatation operator in gauge theories
• Twist-3 light-cone distribution amplitudes of the scalar mesons within the QCD sum rules and their application to the $B\to S$ transition form factors
• Canonical Formulation of $O(N)$ Vector/Higher Spin Correspondence
• Impact of the higher twist effects on the $\gamma {\gamma }^{\ast }\to {\pi }^0$ transition form factor
• Conformal symmetry of the Lange-Neubert evolution equation
• Light front distribution of the chiral condensate
• Renormalon approach to higher-twist distribution amplitudes and the convergence of the conformal expansion
• Parton physics from a heavy-quark operator product expansion: Formalism and Wilson coefficients
• Three-point energy correlators and the celestial block expansion
• Light-Cone Distribution Amplitudes for the Light $1^1{P}_1$ Mesons
• Non-abelian infrared divergences on the celestial sphere
• Two-loop conformal generators for leading-twist operators in QCD
• On level crossing in conformal field theories
• Four loop reciprocity of twist two operators in N=4 SYM
• New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
• Nonperturbative scales in AdS/CFT
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• On the light-ray algebra in conformal field theories
• Deeply virtual Compton scattering beyond next-to-leading order: the flavor singlet case
• Pion transition form factor and distribution amplitudes in large-Nc Regge models
• QCD evolution of entanglement entropy
• N=2 Super Yang-Mills and the XXZ spin chain
• Transition distribution amplitudes and hard exclusive reactions with baryon number transfer
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
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• Light-cone distribution amplitudes of a light baryon in large-momentum effective theory
• Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the second moment of the pion distribution amplitude
• Dual parametrization of generalized parton distributions in two equivalent representations
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• The singlet contribution to the Bjorken sum rule for polarized deep inelastic scattering
• Evolution Equation for Generalized Parton Distributions
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• Diffractive production of two rho^0_L mesons in e^+e^- collisions
• Generalizing event shapes: In search of lost collider time
• Double charmonium production at B-factories within light cone formalism
• Integrability of the evolution equations for heavy-light baryon distribution amplitudes
• Superconformal operators in Yang-Mills theories on the light-cone
• On exact overlaps in integrable spin chains
• Chiral Dynamics and S-wave contributions in Semileptonic $D_s/B_s$ decays into ${\pi }^{+}{\pi }^{-}$
• Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
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• Next-to-leading-power kinematic corrections to DVCS: a scalar target
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• From correlation functions to event shapes in QCD
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• Higher twist distribution amplitudes of the pion and electromagnetic form factor $F_{\pi }(Q^2)$
• Renormalisation of heavy-light light ray operators
• Adler Function, DIS sum rules and Crewther Relations
• Study of $\mathbf{D}\to {\mathbf{a}}_0(980){\mathbf{e}}^{+}{\mathbf{\nu }}_{\mathbf{e}}$ decay in the light-cone sum rules approach
• Two-loop evolution equations for light-ray operators
• Light-cone distribution amplitudes of light mesons with QED effects
• Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit
• Definition and evolution of transverse momentum dependent distribution of twist-three
• Renormalization and non-renormalization of scalar EFTs at higher orders
• Renormalization of twist-four operators in light-cone gauge
• On Local and Integrated Stress-Tensor Commutators
• Three-particle contributions to the renormalisation of B-meson light-cone distribution amplitudes
• Lightcone and quasi distribution amplitudes for light octet and decuplet baryons
• Model-Independent Results for SU(3) Violation in Twist-3 Light-Cone Distribution Functions
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• Integrability in heavy quark effective theory
• Exact scattering amplitudes in conformal fishnet theory
• One-loop hexagon integral to higher orders in the dimensional regulator
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• New Results in Light-Front Phenomenology
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• Second moment of the pion's distribution amplitude
• Electroproduction of tensor mesons in QCD
• Diphoton Generalized Distribution Amplitudes
• Dual conformal symmetry on the light-cone
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• The analytical singlet ${\alpha }_s^4$ QCD contributions into the $e^{+}{e}^{-}$-annihilation Adler function and the generalized Crewther relations
• $B$-to-Glueball form factor and Glueball production in $B$ decays
• Conformal Symmetry as a Template for QCD
• Parton interaction in super Yang Mills theory
• Renormalization of the next-to-leading-power $\gamma \gamma \to h$ and $gg\to h$ soft quark functions
• Operator mixing in massless QCD-like theories and Poincare'-Dulac theorem
• OPE in planar QCD from integrability
• Factorizing the hard and soft spectator scattering contributions for the nucleon form factor F_1 at large Q^2
• Indications of the possible observation of the lowest-lying 1^{-+} QCD state
• The dual parametrization for gluon GPDs
• Higher Twists
• OPE and a low-energy theorem in QCD-like theories
• Instanton corrections to twist-two operators
• Amplitudes from anomalous superconformal symmetry
• Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders
• The $\{\beta \}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O({\alpha }_s^4)$
• QCD cusp anomalous dimension: current status
• Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory
• Semi-inclusive hadronic B decays in the endpoint region
• Reciprocity and integrability in the sl(2) sector of N=4 SYM
• Renormalisation of Composite Operators in Lattice Perturbation Theory with Clover Fermions: Non-forward Matrix Elements
• Light-Front Holographic QCD and Color Confinement
• From Spinning Primaries to Permutation Orbifolds
• B $\to f_2(1270)$ form factors with light-cone sum rules
• The gravity dual of Lorentzian OPE blocks
• Properties of Axial-vector Mesons and Charmless B Decays: B -> VV, VA, AA
• Leading SU(3) breaking in lightcone distribution amplitudes
• Study of f_0(980) and f_0(1500) from B_s \to f_0(980)K, f_0(1500)K Decays
• On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory
• Finite-t and target mass corrections in off-forward hard reactions
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• Basis transformation properties of anomalous dimensions for hard exclusive processes
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• Holomorphic primary fields in free CFT4 and Calabi-Yau orbifolds
• Nonresonant renormalization scheme for twist-$2$ operators in SU($N$) Yang-Mills theory
• Covariant analysis of electromagnetic current on the light cone: exposition with scalar Yukawa theory
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• Invisible and Semi-invisible Decays of Bottom Baryons
• The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Study of f_0(980) and f_0(1500) from B_s \to f_0(980)π, f_0(1500)πDecays
• Exploring the exclusive decay $B^{+}\to \omega {\ell }^{+}\nu$ with light-cone sum rules
• Jet Physics from Static Charges in AdS
• Superfield twist-$2$ operators in $\mathcal{N}=1$ SCFTs and their renormalization-group improved generating functional in $\mathcal{N}=1$ SYM theory
• Applications of Light-Front QCD
• Hard exclusive processes and higher-order QCD corrections
• Charged and Neutral ${\bar{B}}_{u,d,s}\to \gamma$ Form Factors from Light Cone Sum Rules at NLO
• Analytical calculation of heavy quarkonia production processes in computer
• On the Stress Tensor Light-ray Operator Algebra
• Scale-dependence of the $B$-meson LCDA beyond leading order from conformal symmetry
• Operator mixing, UV asymptotics of nonplanar/planar $2$-point correlators, and nonperturbative large-$N$ expansion of QCD-like theories
• The inclusive production of charged pion pairs in proton-antiproton collisions
• Conformal anomaly of pseudo-scalar operators
• One-loop Renormalisation of Lattice QCD Operators for Non-forward Matrix Elements: From Clover to Overlap Fermions
• Light-cone sum rule approach for Baryon form factors
• Strings from large charged fields
• Branching fraction, $CP$ asymmetry, and polarization in $B\to \rho \rho$ decays with the modified perturbative QCD approach
• QCD evolution equations from conformal symmetry
• Transition form factors for $D/B$ to $a_0(980)$ from light-cone QCD sum rules
• Non-leptonic B-decays in and beyond QCD Factorisation
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point