AdS3 correlators and Selberg integrals

IGURI, S.

Lisboa

Conferencia; Mathematical Physics Seminars (GFMUL); 2011

Instituto para a Investigacao Interdisciplinar da Universidade de Lisboa

In this talk I will present some advances in the study spectral flow preserving four-point correlation functions in the AdS3-WZNW model using the Coulomb gas method on the sphere. I will present a multiple integral realization of the conformal blocks and explicitly compute amplitudes involving operators with quantized values of the sum of their spins, i.e., requiring an integer number of screening charges of the first kind. The result is given as a sum over the independent configurations of screening contours yielding a monodromy invariant expansion in powers of the worldsheet moduli. Then I will examine the factorization limit and show that the leading terms in the sum can be identified, in the semiclassical limit, with products of spectral flow conserving three-point functions. These terms can be rewritten as the m-basis version of the integral expression obtained by J. Teschner from a postulate for the operator product expansion of normalizable states in the H+3-WZNW model. Finally, I will determine the equivalence between the factorizations of a particular set of four-point functions into products of two three-point functions either preserving or violating spectral flow number conservation. Based on this analysis it is possible to argue that the expression for the amplitude as an integral over the spin of the intermediate operators holds beyond the semiclassical regime, thus corroborating that spectral flow conserving correlators in the AdS3-WZNW model are related by analytic continuation to correlation functions in the H+3-WZNW model.