Defect Conformal Blocks from Appell Functions

Abstract

We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the case of two bulk and one defect field requires Appell's function $F_4$.

v2: matches published version + two typos corrected

References in corpus (5)

• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• 3d Abelian Gauge Theories at the Boundary
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs

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• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Renormalization group flows in AdS and the bootstrap program
• Universal Spinning Casimir Equations and Their Solutions
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block