Abstract
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 supersymmetries, 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 $1/\sqrt{6}$ 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.
Highlights
Have been extended to many other families of supersymmetric, or merely extremal black holes, and even near-extremal black holes
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 [10] we have argued that if one relaxes one more symmetry one can construct smooth horizonless superstratum solutions that depend on arbitrary continuous functions of two variables, and it is the purpose of this paper to argue that the perturbative semi-classical quantization of superstrata yields a black-holelike entropy growth, and that in the fully back-reacted regime all the three-charge black-hole entropy might be reproduced by space-time fluctuation modes of the superstrata
Summary
The superstratum is a smooth, horizonless soliton (a microstate geometry) that is. -BPS (preserving 4 supersymmetries), depends on several arbitrary functions of two variables and has the same charges as the D1-D5-P black hole. Since the superstratum locally resembles a D1-D5 supertube with a KKM dipole charge, the fully back-reacted superstratum solution should be smooth and be a microstate geometry. An arbitrary profile and the second transition can, in principle, be done independently and locally on each D1-D5 segment, it seems plausible [10] that two supertube transitions could give rise to a smooth superstratum solution that can be parametrized by functions of two variables. The second way to think of a superstratum is to begin with a D1-D5 supertube with KKM dipole charge (parametrized by several arbitrary functions of one variable) and start adding momentum to it. Within the D1-D5 CFT, the left-moving excitations in the space-time directions are correlated with fermionic excitations that only carry SU(2)L quantum numbers.1 It is this that places restrictions on the BPS modes and upon the perturbative shape fluctuations. This perturbative approach to superstrata has been developed in [35, 36] and very simple, restricted classes of fully back-reacted solutions were described in [38]
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