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 $F_4$.

arXiv commentv2: matches published version + two typos corrected

References in corpus (35)

• Conformal Partial Waves and the Operator Product Expansion
• The Bootstrap Program for Boundary CFT_d
• Conformal Field Theories Near a Boundary in General Dimensions
• Conformal Partial Waves: Further Mathematical Results
• Boundary and Interface CFTs from the Conformal Bootstrap
• Energy Momentum Tensor in Conformal Field Theories Near a Boundary
• Weight Shifting Operators and Conformal Blocks
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Multipoint Conformal Blocks in the Comb Channel
• Superintegrability of $d$-dimensional Conformal Blocks
• Universality at large transverse spin in defect CFT
• Line and surface defects for the free scalar field
• An Analytic Approach to BCFT${}_d$
• Analytic Bootstrap for Boundary CFT
• Line defects and radiation in $\mathcal{N}=2$ theories
• Harmony of Spinning Conformal Blocks
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Superconformal surfaces in four dimensions
• Spinning operators and defects in conformal field theory
• From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models
• 3d Abelian Gauge Theories at the Boundary
• Bootstrapping boundary-localized interactions
• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• Radial coordinates for defect CFTs
• From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks
• Calogero-Sutherland Approach to Defect Blocks
• Spinning conformal defects
• Crossing Kernels for Boundary and Crosscap CFTs
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• Multichannel Conformal Blocks for Polygon Wilson Loops
• Superconformal Blocks: General Theory
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Conformal Group Theory of Tensor Structures
• Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs

Cited by in corpus (9)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• 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