Non-supersymmetric microstates of the D1-D5-KK system

TL;DR

The paper constructs a discrete family of smooth non-supersymmetric three-charge geometries carrying D1, D5 and KK monopole charges, embedded in Type IIB on a six-torus and asymptotically flat in four dimensions. Starting from an over-rotating vacuum seed, the authors employ an $ ext{SO}(2,1)$-generated deformation within the $ ext{SL}(3,R)$ framework to include KK charges, then apply a comprehensive chain of boosts, dualities, and gauge transformations to generate D1/D5 charges, all while enforcing regularity conditions to obtain horizonless solitons. They demonstrate the absence of horizons and closed timelike curves, analyze the ergoregion (which vanishes in four dimensions), and explore near-core AdS$_3 imes$S$^3$ decoupling limits, situating these solitons as candidate microstates for the four-dimensional D1-D5-KK black hole. The work provides explicit charge relations, smoothness constraints, and a detailed four-dimensional description, linking the higher-dimensional construction to a four-dimensional microstate picture beyond the half-BPS atom paradigm. Together, these results extend the landscape of non-supersymmetric microstate geometries and offer a concrete path toward their microscopic interpretation and stability analysis.

Abstract

We construct a discrete family of smooth non-supersymmetric three charge geometries carrying D1 brane, D5 brane and Kaluza-Klein monopole charges in Type IIB supergravity compactified on a six-torus, which can be interpreted as the geometric description of some special states of the brane system. These solutions are asymptotically flat in four dimensions, and generalise previous supersymmetric solutions. The solutions have a qualitatively similar structure to previous non-supersymmetric smooth solutions carrying D1 and D5 brane charges in five dimensions, and indeed can be viewed as the five-dimensional system placed at the core of a Kaluza-Klein monopole. The geometries are smooth, free of horizons and do not have closed timelike curves. One notable difference from the five-dimensional case is that the four-dimensional geometry has no ergoregion.