Calogero-Sutherland Approach to Defect Blocks

TL;DR

This paper links conformal defect blocks in conformal field theory to Calogero-Sutherland integrable systems, enabling new mathematical tools and results for analyzing defect-related correlators.

Contribution

It introduces a systematic Calogero-Sutherland framework for conformal defect blocks, extending previous work and connecting to advanced hypergeometric functions.

Findings

Derived new relations between defect blocks and scalar four-point blocks.

Established a Euclidean inversion formula for defect correlators.

Connected defect conformal blocks to integrable multi-particle systems.

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.