Fuzzballs with internal excitations

TL;DR

<3-5 sentence high-level summary> The paper constructs general 2-charge D1-D5 fuzzball geometries with internal excitations on $T^4$ and $K3$, using dualities from F1-P solutions to obtain horizon-free, non-singular spacetimes and expressing them in terms of harmonic data that encode internal curves. Through KK holography, the internal excitations are shown to be captured by vevs of chiral primaries associated with the middle cohomology of the compactification manifold, and each geometry is dual to a specific superposition of Ramond ground states determined by the curves’ Fourier coefficients. The authors compute the holographic vevs and demonstrate selection rules requiring common frequencies between internal and transverse excitations, thereby illuminating the geometry/microstate dictionary and testing the consistency of the fuzzball program within supergravity. They also discuss limitations of a purely supergravity description, arguing that microstates with small or zero R-charge are not well captured by smooth supergravity geometries and may require stringy corrections or representative-ensemble approaches.

Abstract

We construct general 2-charge D1-D5 horizon-free non-singular solutions of IIB supergravity on T^4 and K3 describing fuzzballs with excitations in the internal manifold; these excitations are characterized by arbitrary curves. The solutions are obtained via dualities from F1-P solutions of heterotic and type IIB on T^4 for the K3 and T^4 cases, respectively. We compute the holographic data encoded in these solutions, and show that the internal excitations are captured by vevs of chiral primaries associated with the middle cohomology of T^4 or K3. We argue that each geometry is dual to a specific superposition of R ground states determined in terms of the Fourier coefficients of the curves defining the supergravity solution. We compute vevs of chiral primaries associated with the middle cohomology and show that they indeed acquire vevs in the superpositions corresponding to fuzzballs with internal excitations, in accordance with the holographic results. We also address the question of whether the fuzzball program can be implemented consistently within supergravity.