Calogero-Sutherland Approach to Defect Blocks

Abstract

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recent observation in 1602.01858 and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies of conformal defects. Applications range from several new relations with scalar four-point blocks to a Euclidean inversion formula for defect correlators.

v2: changes for clarity

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Cited by in corpus (30)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Line and surface defects for the free scalar field
• Analytic Bootstrap for Boundary CFT
• Spinning operators and defects in conformal field theory
• Spin Impurities, Wilson Lines and Semiclassics
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Monodromy Defects from Hyperbolic Space
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• Analytic bootstrap for the localized magnetic field
• A dispersion relation for defect CFT
• Free energy and defect $C$-theorem in free scalar theory
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Conformal dispersion relations for defects and boundaries
• N-point spherical functions and asymptotic boundary KZB equations
• Superconformal Blocks: General Theory
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Conformal Group Theory of Tensor Structures
• Fusion of conformal defects in four dimensions
• Renormalization group flows in AdS and the bootstrap program
• Defect Conformal Blocks from Appell Functions
• Analytic bootstrap for magnetic impurities
• Universal Spinning Casimir Equations and Their Solutions
• Bi-Hamiltonian structure of a dynamical system introduced by Braden and Hone
• The gravity dual of Lorentzian OPE blocks
• A novel class of translationally invariant spin chains with long-range interactions
• On ${\mathrm{SQED}}_3$ and ${\mathrm{SQCD}}_3$: phase transitions and integrability
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM