Global conformal blocks via shadow formalism

Abstract

We study \U0001d530\U0001d5292 and \U0001d530\U0001d5293 global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro and \U0001d4b23 conformal field theories in the large central charge limit. In the \U0001d530\U0001d5292 case, we demonstrate that the shadow formalism yields the known expressions in terms of conformal partial waves. Then, we extend this approach to the \U0001d530\U0001d5293 case and show that it allows to build simple integral representations for \U0001d530\U0001d5293 global blocks. We demonstrate this construction on two examples: the four-point block on the sphere and the one-point torus block.