We quantize the D1-D5-P microstate geometries known as superstrata directly in supergravity. We use Rychkov's consistency condition [hep-th/0512053] which was derived for the D1-D5 system; for superstrata, this condition turns out to be strong enough to fix the symplectic form uniquely. For the $(1,0,n)$ superstrata, we further confirm this quantization by a bona-fide explicit computation of the symplectic form using the semi-classical covariant quantization method in supergravity. We use the resulting quantizations to count the known supergravity superstrata states, finding agreement with previous countings that the number of these states grows parametrically smaller than those of the corresponding black hole.

中文翻译：

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计算超重力中的D1-D5-P微态

我们直接在超重力中量化称为超地层的D1-D5-P微状态几何。我们使用Rychkov的一致性条件[hep-th / 0512053]，该条件是针对D1-D5系统得出的；对于超地层来说，这种条件足够强大，可以唯一地固定辛形式。对于$（1,0，n）$超地层，我们通过在超重力中使用半经典协方差量化方法对辛形式的真实显式计算来进一步确认此量化。我们使用所得的量化值来计算已知的超重力超地层状态，并与先前的计算结果相符，即这些状态的数量在参数上小于相应的黑洞的数量。