Black hole formation at the correspondence point

We study the process of bound state formation in a D-brane collision. We consider two mechanisms for bound state formation. The first, operative at weak coupling in the worldvolume gauge theory, is pair creation of W-bosons. The second, operative at strong coupling, corresponds to formation of a large black hole in the dual supergravity. These two processes agree qualitatively at intermediate coupling, in accord with the correspondence principle of Horowitz and Polchinski. We show that the size of the bound state and time scale for formation of a bound state agree at the correspondence point. The time scale involves matching a parametric resonance in the gauge theory to a quasinormal mode in supergravity.

Figure 1

Colliding stacks of 0-branes with relative velocity $v$ and impact parameter $b$.

Figure 2

The imaginary part of the Mathieu characteristic exponent as a function of $a=2q$.

Figure 3

A collapsing shell of 0-branes. Initially the 0-branes are spread uniformly over an $S^8$ with velocities toward the center.

Figure 4

The 0-branes are spread over an $S^8$ of radius $U$. The green $S^7$ has radius $U\sin \theta$ and the red W boson has length $2U\sin \theta /2$.

Figure 5

On the left, the W-boson number density $\frac{1}{N}\frac{dn}{d\theta }$. On the right, the W-boson mass density $\frac{1}{NU}\frac{dm}{d\theta }$.