Bootstrapping multi-wound twist effects in symmetric orbifold CFTs

A bstract We investigate the effects of the twist-2 operator in 2D symmetric orbifold CFTs. The twist operator can join together a twist- M state and a twist- N state, creating a twist-( M + N ) state. This process involves three effects: pair creation, propagation, and contraction. We study these effects by using a Bogoliubov ansatz and conformal symmetry. In this multi-wound scenario, pair creation no longer decouples from propagation, in contrast to the previous study where M = N = 1. We derive equations for these effects, which organize themselves into recursion relations and constraints. Using the recursion relations, we can determine the infinite number of coefficients in the effects through a finite number of inputs. Moreover, the number of required inputs can be further reduced by applying constraints.