Non-BPS Bubbling Geometries in AdS$_3$

TL;DR

This paper constructs and analyzes non-BPS, smooth, horizonless geometries in AdS$_3$ supergravity, revealing an integrable structure and potential dual non-supersymmetric operators in the D1-D5 CFT.

Contribution

It introduces a method to generate non-BPS geometries in AdS$_3$ using Ernst equations and solution-generating techniques, expanding the understanding of non-supersymmetric states in supergravity.

Findings

Constructed large classes of non-BPS geometries supported by electromagnetic flux.

Identified an integrable structure via Ernst equations for these geometries.

Connected non-extremal BTZ black holes with regular bolt solutions.

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.