Supergravity Solution for M5-brane Intersection

TL;DR

The paper constructs a linearized eleven-dimensional supergravity solution for two intersecting M5-branes, with the branes localized in their relative transverse directions and delocalized along the overall transverse directions. The construction proceeds through a Hashimoto origami framework, unfolding the intersecting configuration into D4/D6 setups via Taub-NUT geometry and performing a chain of dualities to reach M-theory, where the solution is governed by a linear Laplace-type equation for a master function $H$ in the background determined by a holomorphic data $ au(z)$. The resulting configurations include an M5-brane on a holomorphic cycle of Taub-NUT or multi-Taub-NUT and a smoothed version of the simple intersection $vw=0$ to $vw=\\epsilon$, both preserving $1/4$ of the supersymmetry. While full localization in all transverse directions is not achieved, the linear structure provides a tractable framework (via $H$) that could enable progression toward fully localized intersecting M5-branes and offers insights for branes on holomorphic cycles in nontrivial geometries. The work also connects to D7/D7-like interpretations upon further compactification and dualities, broadening the avenues for studying worldvolume theories on intersecting branes in curved backgrounds.

Abstract

Supergravity solution describing two intersecting M5-branes is presented. The branes are fixed in the relative transverse directions and are delocalized along the overall transverse ones. The intersection can be smoothed, so that the M5-branes present one holomorphic cycle. We also obtain a solution corresponding to an M5-brane on a holomorphic cycle of multi-Taub-NUT space. All these solutions preserve 1/4 of supersymmetry.