Coulomb integrals and conformal blocks in the AdS3-WZNW model

TL;DR

This paper analyzes four-point correlation functions in the AdS3-WZNW model using Coulomb gas methods, revealing their relation to H3+-WZNW model correlators and providing explicit integral representations of conformal blocks.

Contribution

It introduces a multiple integral realization of conformal blocks for spectral flow preserving four-point functions in the AdS3-WZNW model, connecting them to known H3+-WZNW correlators.

Findings

Explicit integral expressions for conformal blocks are derived.

Leading terms in the semiclassical limit match products of three-point functions.

Spectral flow preserving correlators are related to H3+-WZNW correlators via analytic continuation.

Abstract

We study spectral flow preserving four-point correlation functions in the AdS3-WZNW model using the Coulomb gas method on the sphere. We present a multiple integral realization of the conformal blocks and explicitly compute amplitudes involving operators with quantized values of the sum of their spins, i.e., requiring an integer number of screening charges of the first kind. The result is given as a sum over the independent configurations of screening contours yielding a monodromy invariant expansion in powers of the worldsheet moduli. We then examine the factorization limit and show that the leading terms in the sum can be identified, in the semiclassical limit, with products of spectral flow conserving three-point functions. These terms can be rewritten as the m-basis version of the integral expression obtained by J. Teschner from a postulate for the operator product expansion of normalizable states in the H3+-WZNW model. Finally, we determine the equivalence between the factorizations of a particular set of four-point functions into products of two three-point functions either preserving or violating spectral flow number conservation. Based on this analysis we argue that the expression for the amplitude as an integral over the spin of the intermediate operators holds beyond the semiclassical regime, thus corroborating that spectral flow conserving correlators in the AdS3-WZNW model are related by analytic continuation to correlation functions in the H3+-WZNW model.