Fusion rules and four-point functions in the AdS3 WZNW model

TL;DR

This paper analyzes the operator product expansion and fusion rules in the AdS3 WZNW model, establishing their closure and consistency through spectral flow and four-point function analysis.

Contribution

It introduces a method to compute the OPE in the AdS3 WZNW model via analytic continuation from H3+ and demonstrates the necessity of truncation for algebraic closure.

Findings

Fusion rules close on the Hilbert space due to spectral flow symmetry.

Four-point functions obey spectral flow selection rules.

Truncation is essential for the consistency of physical amplitudes.

Abstract

We study the operator product expansion in the AdS$_3$ WZNW model. The OPE of primary fields and their spectral flow images is computed from the analytic continuation of the expressions in the H$_3^+$ WZNW model, adding spectral flow. We argue that the symmetries of the affine algebra require a truncation which establishes the closure of the fusion rules on the Hilbert space of the theory. Although the physical mechanism determining the decoupling is not completely understood, we present several consistency checks on the results. A preliminary analysis of factorization allows to obtain some properties of four-point functions involving fields in generic sectors of the theory, to verify that they agree with the spectral flow selection rules and to show that the truncation must be realized in physical amplitudes for consistency.