Global conformal blocks via shadow formalism

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.