Coulomb integrals and conformal blocks in the AdS3-WZNW model

SERGIO IGURI Y CARMEN NÚÑEZ

JOURNAL OF HIGH ENERGY PHYSICS

SPRINGER

Lugar: Bristol, United Kingdom; Año: 2009 vol. 2009 p. 1 - 34

1126-6708

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 multipleintegral realization of the conformal blocks and explicitly compute amplitudes involvingoperators with quantized values of the sum of their spins, i.e., requiring an integer numberof screening charges of the first kind. The result is given as a sum over the independentconfigurations of screening contours yielding a monodromy invariant expansion in powersof the worldsheet moduli. We then examine the factorization limit and show that theleading terms in the sum can be identified, in the semiclassical limit, with products ofspectral flow conserving three-point functions. These terms can be rewritten as the m-basisversion of the integral expression obtained by J. Teschner from a postulate for the operatorproduct expansion of normalizable states in the H+3 -WZNW model. Finally, we determinethe equivalence between the factorizations of a particular set of four-point functions intoproducts of two three-point functions either preserving or violating spectral flow numberconservation. Based on this analysis we argue that the expression for the amplitude as anintegral over the spin of the intermediate operators holds beyond the semiclassical regime,thus corroborating that spectral flow conserving correlators in the AdS3-WZNW model arerelated by analytic continuation to correlation functions in the H+3 -WZNW model.