Non-supersymmetric smooth geometries and D1-D5-P bound states

TL;DR

This work constructs new smooth non-supersymmetric solitons carrying D1, D5, and momentum charges in type IIB supergravity on $T^4\times S^1$, extending prior SUSY solutions. Starting from the general nonextremal rotating three-charge black hole family, the authors impose regularity to produce solitons labeled by integers $(m,n)$, with optional $\mathbb{Z}_k$ orbifolds yielding further families; these geometries admit both asymptotically flat and AdS$_3\times S^3$ cores, linking to CFT via spectral flow and orbifold states. They analyze regularity, CFT interpretation, and wave propagation, finding that non-supersymmetric solitons can be matched to CFT states in many cases, though a persistent mismatch in timing delays and the presence of ergoregions (without superradiance for free fields) raise important questions about the full microstate–geometry correspondence. Overall, the results broaden the landscape of smooth microstate geometries beyond supersymmetry and offer new tests of the D1-D5-CFT dictionary and the role of nonperturbative stringy effects in black hole microphysics.

Abstract

We construct smooth non-supersymmetric soliton solutions with D1-brane, D5-brane and momentum charges in type IIB supergravity compactified on T^4 x S^1, with the charges along the compact directions. This generalises previous studies of smooth supersymmetric solutions. The solutions are obtained by considering a known family of U(1) x U(1) invariant metrics, and studying the conditions imposed by requiring smoothness. We discuss the relation of our solutions to states in the CFT describing the D1-D5 system, and describe various interesting features of the geometry.

Figures (1)

• Figure 1: The values of the dimensionless quantities $a_2/\sqrt{M}, a_1/\sqrt{M}$ for which smooth solitons are obtained are indicated by points. The highest point on the figure corresponds to $m=2, n=0$. Increasing $n$ moves diagonally downwards towards the diagonal, and increasing $m-n$ moves down towards $(0,1)$. For each point, there is a set of orbifolds labelled by $k$. Solutions with event horizons exist in the region $a_1/\sqrt{M} + a_2/\sqrt{M} < 1$ (off the bottom of the plotted region).