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Modules for a vertex operator algebra can be twisted by an automorphism of the vertex operator algebra. Intertwining operators among twisted modules describe how a twisted module can act on another twisted module, analogous to how the vertex operator algebra acts on itself.

It is believed that products of twisted intertwining operators should converge, under suitably nice conditions, as they describe 4-point correlation functions in orbifold conformal field theory. Following Yi-Zhi Huang’s method for proving convergence of products of (untwisted) intertwining operators, we obtain new differential equations for products of certain types of twisted intertwining operators after deriving a new Jacobi identity for them. Physically, the correlation functions we have proved to converge describe how chiral fields from the untwisted sector act on a single chiral twisted sector.