Journey to the Center of the Fuzzball

TL;DR

This paper investigates two-charge fuzzball geometries, highlighting the importance of the duality frame, and distinguishes regimes where smooth solutions are valid versus those requiring stringy sources or CFT descriptions.

Contribution

It clarifies the conditions under which smooth fuzzball geometries are valid, emphasizing the role of angular momentum and the comparison of key radii in the geometry.

Findings

Smooth geometries are valid for non-zero angular momentum.

Typical states are better approximated by geometries with stringy sources or free CFT.

The validity of fuzzball solutions depends on the relation between three characteristic radii.

Abstract

We study two-charge fuzzball geometries, with attention to the use of the proper duality frame. For zero angular momentum there is an onion-like structure, and the smooth D1-D5 geometries are not valid for typical states. Rather, they are best approximated by geometries with stringy sources, or by a free CFT. For non-zero angular momentum we find a regime where smooth fuzzball solutions are the correct description. Our analysis rests on the comparison of three radii: the typical fuzzball radius, the entropy radius determined by the microscopic theory, and the breakdown radius where the curvature becomes large. We attempt to draw more general lessons.