Non-BPS Bubbling Geometries in AdS${}_3$

Abstract

We construct large classes of non-BPS smooth horizonless geometries that are asymptotic to AdS${}_3\times$S${}^3\times$T${}^4$ in type IIB supergravity. These geometries are supported by electromagnetic flux corresponding to D1-D5 charges. We show that Einstein equations for systems with eight commuting Killing vectors decompose into a set of Ernst equations, thereby admitting an integrable structure. This feature, which can a priori be applied to other AdS${}_D\times \mathcal{C}$ settings in supergravity, allows us to use solution-generating techniques associated with the Ernst formalism. We explicitly derive solutions by applying the charged Weyl formalism that we have previously developed. These are sourced internally by a chain of bolts that correspond to regions where the orbits of the commuting Killing vectors collapse smoothly. We show that these geometries can be interpreted as non-BPS T${}^4$ and S${}^3$ deformations on global AdS${}_3\times$S${}^3\times$T${}^4$ that are located at the center of AdS${}_3$. These non-BPS deformations can be made arbitrarily small and should therefore correspond to non-supersymmetric operators in the D1-D5 CFT. Finally, we also construct interesting bound states of non-extremal BTZ black holes connected by regular bolts.

52 pages + Appendix, 16 figures; v2: minor changes and published version

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