Superstrata on Orbifolded Backgrounds

Some microstates of the Strominger-Vafa black hole are represented by smooth horizonless geometries called superstrata. The standard superstrata are deformations of ${\rm AdS}_3\times S^3$, but there are also generalizations of superstrata on the orbifold $({\rm AdS}_3\times S^3)/\mathbb{Z}_p$. In this paper, we discuss aspects of such orbifolded superstrata. We present a CFT perspective on the structure of orbifolded superstrata, showing that they can be constructed in a $p$-covering space of the orbifold CFT just as the standard superstrata. We also explicitly write down and study the geometry of the orbifolded superstrata, focusing on the difference from the non-orbifold case, $p=1$. We discuss further generalization of superstrata to the ones on a fractional spectral flow of $({\rm AdS}_3\times S^3)/\mathbb{Z}_p$. This generalization involves new fractional mode excitations of the CFT side. We estimate the number of those generalized superstrata, and show that their entropy is too small to account for the Strominger-Vafa entropy. We will discuss some implications of this result, related to the typical microstates of the black hole and the relevant supersymmetry index.