Covering space maps for n-point functions with three long twists

Orbifold CFTs are constructed by quotienting a given CFT by a discrete global symmetry Γ. After the quotient, twisted sector states and corresponding operators appear in the theory. Permutation orbifolds are constructed by considering a seed CFT, copying it N times, and then orbifolding by a global symmetry Γ (often taken to be S_N) which acts by permuting the fields and operators of the N copies of the seed CFT. For permutation orbifolds, one may use the covering space technique to calculate correlators of operators in the twisted sector. The central problem in this technique is to find a many sheeted cover of the the base space on which the orbifold CFT is defined, along with the corresponding covering space map. The branch points in the map implement the twisted boundary conditions around twisted sector operators, and so the twist sector of the operators in a given correlator define the type of covering space map one seeks. In this talk we consider covering space maps for single cycle twists, and where the base space and the covering space are both spheres. We construct the infinite class of covering space maps relevant for correlators where three of the operators are in twisted sectors corresponding to arbitrarily long cycles, and the remaining twisted sector operators are an arbitrary number of twist-2 operators. These maps are relevant for the deformation of the orbifold point of the D1/D5 CFT, where the deformation operator is in the twist-2 sector.