A Backlund Transformation for Elliptic Four-Point Conformal Blocks
Résumé
We apply an integral transformation to solutions of a partial differential equa-
tion for the five-point correlation functions in Liouville theory on a sphere with
one degenerate field $V_{ − 1/(2b)}$ . By repeating this transformation, we can reach a whole lattice of values for the conformal dimensions of the four other operators. Factorizing out the degenerate field leads to integral representations of the corresponding four-point conformal blocks. We illustrate this procedure on the elliptic conformal blocks discovered in a previous publication.