Larger twists and higher n-point functions with fractional conformal descendants in SN orbifold CFTs at large N

Abstract

Abstract We consider correlation functions in symmetric product (SN) orbifold CFTs at large N with arbitrary seed CFT, expanding on our earlier work [1]. Using covering space techniques, we calculate descent relations using fractional Virasoro generators in correlators, writing correlators of descendants in terms of correlators of ancestors. We first consider the case three-point functions of the form (m-cycle)-(n-cycle)-(q-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In these examples we show that the correlator descent relations make sense in the base space orbifold CFT, but do not depend on the specific details of the seed CFT. This makes these descent relations universal in all SN orbifold CFTs. Next, we explore four-point functions of the form (2-cycle)-(n-cycle)-(n-cycle)-(2-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In such cases a single parameter in the map s parameterizes both the base space cross ratio ζz and the covering space cross ratio ζt. We find that the correlator descent relations for the four point function make sense in the base space orbifold CFT as well, arguing that the dependence on the parameter s is tantamount to writing the descent relations in terms of the base space cross ratio. These descent relations again do not depend on the specifics of the seed CFT, making these universal as well.