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

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.

37 pages, 5 figures, version to appear in Physical Review D

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• String correlators on ${\text{AdS}}_3$: Three-point functions
• Three-point functions in superstring theory on AdS3xS3xT4
• More AdS_3 correlators
• On modular properties of the AdS3 CFT
• On duality and extended chiral symmetry in the SL(2,R) WZW model
• String correlators on ${\text{AdS}}_3$: Four-point functions
• Modular invariant partition functions for non-compact G/Ad(H) models
• The $Ad{S}_3\times S^1$ Chiral Ring
• Inner brane: A D3-brane in the Nappi-Witten model from an inner group automorphism
• Notes on the SL(2,R) CFT
• Strings and D-branes in curved space-time