Supergravity Solutions for Localized Intersections of Branes

TL;DR

Hashimoto develops explicit supergravity solutions for localized brane intersections by orbifolding flat M-brane configurations in $R^{1,10}$ and reducing to Type IIA in the near-horizon geometry of D6-branes, leveraging an ALE space $C^2/Z_N$. The central result is a D4-brane ending on a D6-brane in the near-horizon background, obtained by embedding the M5-brane into the ALE factor and performing the appropriate orbifold and reduction; the construction is then extended to a wider class of holomorphic embeddings, such as curves described by $(v - a w)^N = b^N$, which yield paraboloid-like intersections. While not a universal solution to all localized brane intersections, the explicit backgrounds provide concrete benchmarks and a framework for generating further examples, with implications for RR/NSNS flux structure and potential dualities. The work connects M-theory embeddings, ALE orbifolds, and near-horizon holographic contexts to illuminate how localized intersections can be realized within controlled supergravity solutions and guides future explorations of brane dynamics and gauge/gravity dualities.

Abstract

We construct an explicit supergravity solution for a configuration of localized D4-brane ending on a D6-brane, restricted to the near horizon region of the latter. We generate this solution by dimensionally reducing the supergravity solution for a flat M5-brane in $R^{1,7} \times C^2/Z_N$ with the M5-brane partially embedded in $C^2/Z_N$. We describe the general class of localized intersections and overlaps whose supergravity solutions are constructible in this way.

Figures (1)

• Figure 1: Configuration of branes embedded according to $(v-aw)^N = b^N$ in the natural coordinates of the near horizon D6-brane geometry. Here, $a=1$ indicated by the fact that the paraboloid points along the $U_2$ direction. As $b \rightarrow 0$, the paraboloid degenerates to a "string" like geometry.