Torus shadow formalism and exact global conformal blocks

TL;DR

This paper develops a method using the shadow formalism to compute exact global conformal blocks on the torus in two-dimensional conformal field theory, introducing the necklace function for n-point blocks.

Contribution

It introduces a novel approach to calculating torus conformal blocks via the shadow formalism and defines the necklace function for n-point blocks.

Findings

Derived explicit expressions for torus conformal blocks using the shadow formalism.

Introduced the necklace function as a hypergeometric-type function for n-point torus blocks.

Provided a new computational framework for torus CFT correlators.

Abstract

Using the shadow formalism we find global conformal blocks of torus CFT$_2$. It is shown that $n$-point torus blocks in the ``necklace'' channel (a loop with $n$ legs) are expressed in terms of a hypergeometric-type function which we refer to as the necklace function.