Minisuperspace quantization of bubbling AdS${}_2\times$S${}^2$ geometries

We quantize the moduli space of supersymmetric microstates describing four-dimensional black holes with AdS${}_2$$\times$S${}^2$ asymptotics. To acquire the commutation relations of quantization, we find the symplectic form that is imposed in the Type IIB SUGRA and defined in the space of solutions parameterized by one complex harmonic function in $R^3$ with sources distributed along closed curves.