Abstract
In this article we investigate the structure of the four-point functions of the AdS3-WZNW model. We consider the integral expression for the unflowed four-point correlator involving at least one state in the discrete part of the spectrum derived by analytic continuation from the H 3 + -WZNW model and we show that the conformal blocks can be obtained from those with an extremal-weight state by means of an intertwining operator. We adapt the procedure for dealing with correlators with a single unit of spectral flow charge and we get a factorized integral expression for the corresponding four-point function. We finally transform the formulas back to the space-time picture.
Highlights
In [30] the proposal was verified by computing the modular invariant one-loop partition function for Euclidean BTZ black hole backgrounds, more modular properties of the AdS3WZNW model being further studied in [31, 32]
In this article we investigate the structure of the four-point functions of the AdS3-WZNW model
We consider the integral expression for the unflowed four-point correlator involving at least one state in the discrete part of the spectrum derived by analytic continuation from the H3+-WZNW model and we show that the conformal blocks can be obtained from those with an extremal-weight state by means of an intertwining operator
Summary
An integral factorized expression for the four-point function of the H3+-WZNW model was introduced and intensively studied in [34]. In this paper we prefer to retain the expression of the four-point correlator the simplest as possible and, we will consider a concrete case in which this happens, namely, when at least two external fields, say those at the first and the last insertion points, are assumed to belong to the discrete part of the spectrum If this condition is relaxed by assuming that the correlator has at least one discrete state, the integral (3.23) should be redefined to give account of some additional discrete contributions, but aside of this, none of the results in what follows would be compromised. If this expression gives the correct factorized form for the four-point function, the dependence of the integrand for the leading term as z → 0 must go as |z|2(∆j−∆j1−∆j2), so that Q4(J|M ±|λ) should act trivially if contracted with this factor, and the remaining coefficient should equal Dj(J|M ). Enough, since Q4(J|M ±|λ) does not depend on z, the descendant contributions to the conformal blocks of a given level can be related through (3.44) to those contributions with a lowest or a highest-weight state coming strictly from the descendants of the very same level, i.e., identity (3.44) is realized order by order when formally expanding the generating operators in powers of z
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