Coulomb integrals for the SL(2,R) WZNW model

Abstract

We review the Coulomb gas computation of three-point functions in the SL(2,R) WZNW model and obtain explicit expressions for generic states. These amplitudes have been computed in the past by this and other methods but the analytic continuation in the number of screening charges required by the Coulomb gas formalism had only been performed in particular cases. After showing that ghost contributions to the correlators can be generally expressed in terms of Schur polynomials we solve Aomoto integrals in the complex plane, a new set of multiple integrals of Dotsenko-Fateev type. We then make use of monodromy invariance to analytically continue the number of screening operators and prove that this procedure gives results in complete agreement with the amplitudes obtained from the bootstrap approach. We also compute a four-point function involving a spectral flow operator and we verify that it leads to the one unit spectral flow three-point function according to a prescription previously proposed in the literature. In addition, we present an alternative method to obtain spectral flow non-conserving n-point functions through well defined operators and we prove that it reproduces the exact correlators for n=3. Independence of the result on the insertion points of these operators suggests that it is possible to violate winding number conservation modifying the background charge.

Improved presentation. New section on spectral flow violating correlators and computation of a four-point function

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Cited by in corpus (18)

• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Spectral Flow in AdS(3)/CFT(2)
• String correlators on ${\text{AdS}}_3$: Three-point functions
• Fusion rules and four-point functions in the AdS3 WZNW model
• More AdS_3 correlators
• On spectrally flowed local vertex operators in AdS${}_3$
• On a Selberg-Schur integral
• Critical Non-Abelian Vortex and Holography for Little String Theory
• A twisted FZZ-like dual for the two-dimensional black hole
• On duality and extended chiral symmetry in the SL(2,R) WZW model
• String correlators on ${\text{AdS}}_3$: Four-point functions
• Some recursive formulas for Selberg-type integrals
• The $Ad{S}_3\times S^1$ Chiral Ring
• Notes on the SL(2,R) CFT
• Schur expansion of random-matrix reproducing kernels
• Contour Integral Representations for the Characters of Logarithmic CFTs
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• Strings and D-branes in curved space-time