  We consider correlation functions in symmetric product ($S_N$) orbifold CFTs
at large $N$ with arbitrary seed CFT. Specifically, we consider correlators of
descendant operators constructed using both the full Virasoro generators
$L_{m}$ and fractional Virasoro generators $\ell_{m/n_i}$. Using covering space
techniques, we show that correlators of descendants may be written entirely in
terms of correlators of ancestors, and further that the appropriate set of
ancestors are those operators that lift to conformal primaries on the cover. We
argue that the covering space data should cancel out in such calculations. To
back this claim, we provide some example calculations by considering a
three-point function of the form (4-cycle)-(2-cycle)-(5-cycle) that lifts to a
three-point function of arbitrary primaries on the cover, and descendants
thereof. In these examples we show that while the covering space is used for
the calculation, the final descent relations do not depend on covering space
data, nor on the details of which seed CFT is used to construct the orbifold,
making these results universal.
