General 2 charge geometries

TL;DR

The work addresses the incompleteness of horizon-free two-charge geometries by constructing NS1-P backgrounds that include fermionic condensates in addition to bosonic ones. Using generalized chiral null models, it derives backreacted harmonic functions with dipole-like l=1 sources and natural gauge structures, and discusses how these solutions map to the D1-D5 frame via dualities for microstate counting. The results demonstrate that fermionic bilinears are essential to account for the full entropy and highlight subtle aspects of regularity, AdS/CFT matching, and the interplay between worldsheet symmetries and spacetime diffeomorphisms. These fermionic geometries extend the horizon-free microstate program and guide future work toward three-charge generalizations and bubbling interpretations.

Abstract

Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.