Global conformal blocks via shadow formalism

Abstract

Abstract We study 𝔰𝔩2 and 𝔰𝔩3 global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro and 𝒲3 conformal field theories in the large central charge limit. In the 𝔰𝔩2 case, we demonstrate that the shadow formalism yields the known expressions in terms of conformal partial waves. Then, we extend this approach to the 𝔰𝔩3 case and show that it allows to build simple integral representations for 𝔰𝔩3 global blocks. We demonstrate this construction on two examples: the four-point block on the sphere and the one-point torus block.