Torus shadow formalism and exact global conformal blocks

The talk is devoted to the investigation of the large central charge limit of conformal blocks in two-dimensional conformal field theory with torus topology. I will discuss the application of the shadow formalism of conformal field theory to the computation of global torus blocks. After reviewing the shadow formalism of two-dimensional conformal field theory, it will be shown how the known constructions generalise to conformal field theories on the torus. Using the developed formalism we find multipoint global torus conformal blocks. The found $n$-point blocks are expressed through previously unknown hypergeometric functions of $n$ variables.