A brane teaser

In this note we study the puzzle posed by two M5-branes intersecting on a string (or equivalently, a single M5-brane wrapping a holomorphic four-cycle in Script C⁴). It has been known for a while that this system is different from all other configurations built using self-intersecting M-branes; in particular the corresponding supergravity solution exhibits various curious features which have remained unexplained. We propose that the resolution to these puzzles lies in the existence of a non-zero two-form on the M5-brane world-volume.