Conformal Basis, Optical Theorem, and the Bulk Point Singularity

Abstract

We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators. We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis. In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis. We further discuss the relation between the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are explicitly computed in this basis to demonstrate these results.

31 pages, 3 figures

References in corpus (11)

• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning AdS Propagators
• Gluon Amplitudes as 2d Conformal Correlators
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Local bulk S-matrix elements and CFT singularities
• A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
• String scattering in flat space and a scaling limit of Yang-Mills correlators
• A $d$-Dimensional Stress Tensor for Mink${}_{d+2}$ Gravity
• In search of conformal theories
• Asymptotic Symmetries of Yang-Mills with Theta Term and Monopoles

Cited by in corpus (47)

• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• The Holographic Nature of Null Infinity
• Celestial Amplitudes from UV to IR
• Null Infinity and Unitary Representation of The Poincare Group
• Tree-level gluon amplitudes on the celestial sphere
• AdS Witten Diagrams to Carrollian Correlators
• BMS Symmetry of Celestial OPE
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Conformal Block Expansion in Celestial CFT
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Conformal Blocks from Celestial Gluon Amplitudes
• Lectures on Celestial Holography
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• Notes on flat-space limit of AdS/CFT
• Modified celestial amplitude in Einstein gravity
• Conformal properties of soft-operators - 1 : Use of null-states
• On loop celestial amplitudes for gauge theory and gravity
• Conformal properties of soft operators -- 2 : Use of null-states
• Relativistic partial waves for celestial amplitudes
• Descendants in celestial CFT and emergent multi-collinear factorization
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Four-point correlators of light-ray operators in CCFT
• Pure Supersymmetric AdS and the Swampland
• Bulk locality from the celestial amplitude
• Implications of Superrotations
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial amplitudes in an ambidextrous basis
• Celestial Geometry
• Poincaré Constraints on Celestial Amplitudes
• Celestial insights into the S-matrix bootstrap
• Chaos in Celestial CFT
• Minkowski Conformal Blocks and the Regge Limit for SYK-like Models
• Celestial Mellin Amplitude
• Zwanziger's pairwise little group on the celestial sphere
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Celestial Berends-Giele current
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Correlation functions at the bulk point singularity from the gravitational eikonal S-matrix
• Celestial OPE blocks
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Celestial Regge theory
• Celestial Feynman Rules for Scalars
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle