Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes

TL;DR

This paper classifies solutions in massive IIA supergravity for intersecting D8/D4-branes with fundamental strings, revealing new geometries and showing the absence of certain lower-dimensional CFT solutions.

Contribution

It provides a detailed analysis of BPS solutions with specific symmetries, identifying novel configurations of strings ending on D8-branes and O8-planes, and clarifies the landscape of possible near-horizon geometries.

Findings

Only the $AdS_6$ geometry with enhanced symmetry is found.

Novel solutions for strings ending on D8-branes and O8-planes are identified.

No solutions corresponding to 1+0-dimensional CFTs are found.

Abstract

We consider solutions of massive IIA supergravity corresponding to the half-BPS intersection of D8/D4-branes with fundamental strings. The $1+1$-dimensional intersection preserves the symmetry $D(2,1;\gamma;1) \times SO(4)$. We give a reduction and partial integration of the BPS equations for this symmetry group. We then specialize to the cases of enhanced supersymmetry corresponding to $\gamma = -1/2,-2$ or $\gamma = 1$. In the first case, we show that the only solution with enhanced symmetry is given by the $AdS_6$ geometry describing the near horizon geometry of D8/D4-branes in the presence of an O8-plane. In the second case, we identify novel solutions corresponding to fundamental strings ending on D8-branes and a second set of novel solutions corresponding to fundamental strings ending on an O8-plane. In both cases, the fundamental string geometry contains an asymptotically flat region where the string coupling goes to zero. We also show that there are no solutions corresponding to $1+0$-dimensional CFTs, which one may have hoped to construct by suspending fundamental strings between D8-branes.