A Bäcklund transformation for elliptic four-point conformal blocks

Abstract

We apply an integral transformation to solutions of a partial differential equation for five-point correlation functions in Liouville theory on a sphere with one degenerate field $V_{-\frac{1}{2b}}$. 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.

9 pages, to be published in the Memorial Volume for Ludwig Faddeev

References in corpus (4)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• On the Liouville three-point function
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks