Spectral Flow, and the Spectrum of Multi-Center Solutions

Understand

We discuss "spectral flow" coordinate transformations that take asymptotically four-dimensional solutions into other asymptotically four-dimensional solutions.

• We find that spectral flow can relate smooth three-charge solutions with a multi-center Taub-NUT base to solutions where one or several Taub-NUT centers are replaced by two-charge supertubes, and vice versa.
• We further show that multi-parameter spectral flows can map such Taub-NUT centers to more singular centers that are either D2-D0 or pure D0-brane sources.
• Since supertubes can depend on arbitrary functions, we establish that the moduli space of smooth horizonless black hole microstate solutions is classically of infinite dimension.