Four-twist effects on excitations in symmetric orbifold CFTs

Symmetric orbifold CFTs contain twist operators that can join and split copies of the CFT. In this paper, we study the effects of four twist-2 operators on two copies of a single free boson. A recent study analyzed their effects on the vacuum, finding a nontrivial left-right mixing that arises from the fact that the covering surface is a torus, while the effects of one or two twist-2 operators do not produce such mixing. Here, we extend this analysis to excited states and find a similar left-right mixing. Furthermore, we explore the continuum, or high-energy, limit and show that the left-right mixing becomes negligible in this limit.