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

Understand

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.