Membranes on Calibrations

TL;DR

This paper shows that the constraints for M2-branes forming BPS funnels ending on M5-branes are naturally satisfied within BLG theory due to its algebraic structure, clarifying previous fuzzy funnel constructions.

Contribution

It demonstrates that the consistency conditions for these solutions are automatic in BLG theory, linking calibration conditions with the fundamental identity and supersymmetry.

Findings

Constraints are automatic in BLG theory

Fuzzy funnel constructions are explained via BLG

Role of 3-algebra trace form discussed

Abstract

M2-branes can blow up into BPS funnels that end on calibrated intersections of M5-branes. In this quick note, we make the observation that the constraints required for the consistency of these solutions are automatic in Bagger-Lambert-Gustavsson (BLG) theory, thanks to the fundamental identity and the supersymmetry of the calibration. We use this to explain how the previous ad hoc fuzzy funnel constructions emerge in this picture, and make some comments about the role of the 3-algebra trace form in the derivation.