Five-brane Calibrations and Fuzzy Funnels

TL;DR

This work extends the Basu–Harvey equation to describe membranes ending on five‑branes wrapped on calibrated cycles in M‑theory. By formulating a modified Nahm‑type equation with calibration tensors and a SUSY‑based projector framework, it derives explicit BPS profiles for multiple five‑brane intersections preserving fractions of supersymmetry ($\nu=1/2,1/4,1/8$). It demonstrates that the linearised, Bogomol'nyi‑bound form of the membrane action captures these solutions, and provides matrix realizations using fuzzy spheres and block‑diagonal Spin(4) representations to realise the Calibrated configurations. The results offer a coherent non‑Abelian membrane picture of M2–M5 intersections in calibrated geometries, extending the D1–D3/Constable program to M‑theory calibrations and contributing to the understanding of M‑theory brane dynamics.

Abstract

We present a generalisation of the Basu-Harvey equation that describes membranes ending on intersecting five-brane configurations corresponding to various calibrated geometries.