Smooth geometries with four charges in four dimensions

TL;DR

The authors construct horizonless, rotating four-dimensional geometries carrying D1, D5, KK monopole, and momentum charges by embedding a known five-dimensional microstate into Taub-NUT, using six-dimensional minimal supergravity on a Gibbons-Hawking base. The solution is encoded by six harmonic functions and regularity constraints fix the parameters, yielding a fully explicit, smooth geometry with no horizons and a near-horizon AdS$_3\times$S$^3$ structure. The work clarifies how KK charge can be incorporated into four-dimensional microstate geometries, analyzes orbifold resolutions, and discusses CFT interpretations in the (0,4) context, including a potential link to spectral-flow-like structures. The results extend the microstate program to 4D, providing a concrete, tractable example with controlled regularity and a rich near-horizon geometry, while leaving open questions about bound-state criteria and precise dual CFT mapping.

Abstract

A class of axially symmetric, rotating four-dimensional geometries carrying D1, D5, KK monopole and momentum charges is constructed. The geometries are found to be free of horizons and singulaties, and are candidates to be the gravity duals of microstates of the (0,4) CFT. These geometries are constructed by performing singularity analysis on a suitably chosen class of solutions of six-dimensional minimal supergravity written over a Gibbons-Hawking base metric. The properties of the solutions raise some interesting questions regarding the CFT.