Torus classical conformal blocks

Abstract

After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus, we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing the classical conformal blocks for the sphere topology to the tours topology. We give the explicit results for the classical blocks up to the third-order in the nome included and compare them with the classical limit of the quantum conformal blocks. The extension to higher orders is straightforward.