Black-Hole Entropy from

There are, by now, several arguments that superstrata, which represent D1-D5-P bound states that depend upon arbitrary functions of two variables and that preserve four su-persymmetries, exist in string theory, and that their gravitational back-reaction results in smooth horizonless solutions. In this paper we examine the shape and density modes of the superstratum and give strong evidence that the back-reacted supergravity solution allows for fluctuation modes whose quantization reproduces the entropy growth of black holes as a function of the charges. In particular, we argue that the shape modes of the superstratum that lie purely within the non-compact space-time directions account for at least 1/ 6 of the entropy of the D1-D5-P black hole and propose a way in which the rest of the entropy could be captured by superstratum fluctuations. We complete the picture by conjecturing a relationship between bound states of multiple superstrata and momentum excitations of different twisted sectors of the dual CFT. ar X i