Nonsupersymmetric smooth geometries and D1-D5-P bound states

We construct smooth nonsupersymmetric soliton solutions with D1-brane, D5-brane, and momentum charges in type IIB supergravity compactified on $T^4\times S^1$, with the charges along the compact directions. This generalizes previous studies of smooth supersymmetric solutions. The solutions are obtained by considering a known family of $U(1)\times U(1)$ 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.

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 labeled 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).