Six-dimensional Methods for Four-dimensional Conformal Field Theories

Abstract

The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as projections of fields on the hypercone in six-dimensional projective space, satisfying certain transversality conditions. In this way some Green's functions in conformal field theories are shown to have structures more general than those commonly found by use of the inversion operator. These methods fit in well with the assumption of AdS/CFT duality. In particular, it is transparent that if fields on AdS${}_5$ approach finite limits on the boundary of AdS${}_5$, then in the conformal field theory on this boundary these limits transform with conformal dimensionality zero if they are tensors (of any rank), but with conformal dimension 1/2 if they are spinors or spinor-tensors.

Version accepted for publication in Physical Review D. References to earlier work added in footnote 2. Minor errors corrected. 24 pages

References in corpus (4)

• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• The Standard Model of Particles and Forces in the Framework of 2T-physics
• Gravity in 2T-Physics
• Geometry and Symmetry Structures in 2T Gravity

Cited by in corpus (122)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Projectors, Shadows, and Conformal Blocks
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Spinning Conformal Blocks
• Light-ray operators in conformal field theory
• Spinning AdS Propagators
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Notes on the scattering amplitude / Wilson loop duality
• Boundary Conformal Field Theory and a Boundary Central Charge
• Weight Shifting Operators and Conformal Blocks
• Modular Hamiltonians on the null plane and the Markov property of the vacuum state
• AdS Field Theory from Conformal Field Theory
• A Study of Quantum Field Theories in AdS at Finite Coupling
• TASI lectures on AdS/CFT
• Conformal Collider Physics from the Lightcone Bootstrap
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Conformal algebra: R-matrix and star-triangle relation
• On complexified mechanics and coquaternions
• The Black Hole S-Matrix from Quantum Mechanics
• Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe
• Mellin Amplitudes for Dual Conformal Integrals
• CP-violating CFT and trace anomaly
• Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator
• Strings in AdS_4 x CP^3, Wilson loops in N=6 super Chern-Simons-matter and Bremsstrahlung functions
• Superembedding methods for 4d N=1 SCFTs
• Logarithmic forms and differential equations for Feynman integrals
• Conformal Primary Basis for Dirac Spinors
• Spinning conformal defects
• Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics
• Superembedding Methods for Current Superfields
• Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory
• Twistor methods for AdS${}_5$
• No-go for Partially Massless Spin-2 Yang-Mills
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Six-dimensional Methods for Four-dimensional Conformal Field Theories II: Irreducible Fields
• Manifestly Dual-Conformal Loop Integration
• Conformally compactified Minkowski superspaces revisited
• Conformal Bootstrap in Embedding Space
• Geodesic Witten diagrams with an external spinning field
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Tensors and Spinors in de Sitter Space
• Scale invariance vs conformal invariance
• Symmetry group at future null infinity I: Scalar theory
• Holographic Representation of Local Operators In De Sitter Space
• Building Bases of Loop Integrands
• Mellin Amplitudes for Fermionic Conformal Correlators
• Implications of Superrotations
• Operator product expansion for conformal defects
• Two Point Functions in Defect CFTs
• Fermions in Geodesic Witten Diagrams
• On conformal correlators and blocks with spinors in general dimensions
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Superembedding methods for 4d N-extended SCFTs
• Quantum Integrable Systems from Conformal Blocks
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Geodesic Witten diagrams with anti-symmetric exchange
• Efficient Rules for All Conformal Blocks
• Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory
• Constraints on Interacting Scalars in 2T Field Theory and No Scale Models in 1T Field Theory
• The holographic dual of the Penrose transform
• Generalized Dualities in 1T-Physics as Holographic Predictions from 2T-Physics
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• Lectures on Higher Spin Holography
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• The background field method and critical vector models
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ superconformal field theory
• Quantum quenches during inflation
• Intertwining Operator in Thermal CFT${}_d$
• The Inversion Formula and 6j Symbol for 3d Fermions
• Two-Component Spinorial Formalism using Quaternions for Six-dimensional Spacetimes
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• Higgs phenomenon for higher spin fields on AdS_3
• Conformal mechanics
• On fast quenches and spinning correlators
• Conformal Fields from Neural Networks
• Space-time CFTs from the Riemann sphere
• Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Spinors and the Weyl Tensor Classification in Six Dimensions
• Conformal invariance: from Weyl to SO(2,d)
• The Functional Bootstrap for Boundary CFT
• Ambiguities in the Seiberg-Witten Map and Emergent Gravity
• Simplifying instanton corrections to N=4 SYM correlators
• Further Results on a Function Relevant for Conformal Blocks
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Counting Conformal Correlators
• General Bootstrap Equations in 4D CFTs
• Conformal Lagrangians from the (formal) near boundary analysis of AdS gauge fields
• A Universal Formula for the Stress-Tensor Contribution to Scalar Four-Point Functions
• The Goldstone Equivalence Theorem and AdS/CFT
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Deconstructing Conformal Blocks in 4D CFT
• Spinning Particle Geometries in AdS${}_3$/CFT${}_2$
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Entanglement entropy of a Rarita-Schwinger field in a sphere
• On the Six-dimensional Kerr Theorem and Twistor Equation
• Holographic 2-Point Functions in the Pseudo-Conformal Universe
• Massless spinning particle and null-string on $Ad{S}_d$: projective-space approach
• Conformal correlators in the critical $O(N)$ vector model
• Super Yang-Mills theory in 10+2 dimensions, The 2T-physics Source for N=4 SYM and M(atrix) Theory
• Massive scalar field on (A)dS space from a massless conformal field in ${\mathbb{R}}^6$
• Factorization of Mellin amplitudes
• CFTs on curved spaces
• SO(2,4)-covariant quantization of the Maxwell field in a conformally flat space
• Conformally Invariant Spinorial Equations in Six Dimensions
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Jet Physics from Static Charges in AdS
• Killing Spinors and Related Symmetries in Six Dimensions
• Non-linear effects in early Universe cosmology
• Quantum fields on projective geometries
• Interpolating conformal algebra in $(1+1)$ dimensions between the instant form and the light-front form of relativistic dynamics
• Analytic Studies of Fermions in the Conformal Bootstrap
• Regularization of energy-momentum tensor correlators and parity-odd terms
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography
• Three-point functions of fermionic higher-spin currents in 4D conformal field theory
• Doubled Conformal Compactification