Twisted restricted conformal blocks of vertex operator algebras I: g-twisted correlation functions and fusion rules

Abstract

In this paper, we introduce a notion of g-twisted restricted conformal block on the three-pointed twisted projective line

associated with an untwisted module $M^1$ and the bottom levels of two g-twisted modules $M^2$ and $M^3$ over a vertex operator algebra V. We show that the space of twisted restricted conformal blocks is isomorphic to the space of g-twisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem.