On conformal correlators and blocks with spinors in general dimensions

Abstract

We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For this, the embedding space formalism is employed and the polarisation spinors are introduced to simplify the computations. Three-point functions are rewritten in terms of differential operators acting on scalar-scalar-tensor correlation functions. This enables us to determine conformal blocks for four-point functions with scalar and spinor fields by acting the differential operators on scalar conformal blocks, which will be useful in finding their geodesic Witten diagrams.

21 pages, no figures, references added, typos corrected

References in corpus (11)

• Cosmological Collider Physics
• Spinning AdS Propagators
• A Mellin space approach to the conformal bootstrap
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Spinning Witten Diagrams
• Consistency condition for inflation from (broken) conformal symmetry
• Anatomy of Geodesic Witten Diagrams
• Geodesic Diagrams, Gravitational Interactions & OPE Structures
• Holographic inflation and the conservation of $\zeta$
• Holographic non-Gaussianities in general single-field inflation
• General Bootstrap Equations in 4D CFTs

Cited by in corpus (16)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Momentum space approach to crossing symmetric CFT correlators
• Simplifying large spin bootstrap in Mellin space
• Scalar CFTs and Their Large N Limits
• Conformal Primary Basis for Dirac Spinors
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Tensors and Spinors in de Sitter Space
• Towards Feynman rules for conformal blocks
• Fermions in Geodesic Witten Diagrams
• Conformal partial waves in momentum space
• Conformal Contact Terms and Semi-Local Terms
• On fast quenches and spinning correlators
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Spinors and conformal correlators
• Spinor vertexes and bubbles in the "old" conformal bootstrap on AdS and FMH problem: Yukawa model