Planes, branes and automorphisms: II. Branes in motion

TL;DR

This paper classifies supersymmetric configurations of two M5-branes in motion, revealing new configurations with various preserved supersymmetries and interpreting them through group theory and geometric structures.

Contribution

It completes the classification of moving M5-brane configurations, introducing novel supersymmetric arrangements and their geometric and group-theoretic interpretations.

Findings

Classified supersymmetric two M5-brane configurations with motion.

Identified configurations preserving fractions of supersymmetry up to 1/4.

Connected configurations to Cayley planes and geometric structures.

Abstract

We complete the classification of supersymmetric configurations of two M5-branes, started by Ohta and Townsend. The novel configurations not considered before are those in which the two branes are moving relative to one another. These configurations are obtained by starting with two coincident branes and Lorentz-transforming one of them while preserving some supersymmetry. We completely classify the supersymmetric configurations involving two M5-branes, and interpret them group-theoretically. We also present some partial results on supersymmetric configurations involving an arbitrary number of M5-branes. We show that these configurations correspond to Cayley planes in eight-dimensions which are null-rotated relative to each other in the remaining (2+1) dimensions. The generic configuration preserves 1/32 of the supersymmetry, but other fractions (up to 1/4) are possible by restricting the planes to certain subsets of the Cayley grassmannian. We discuss some examples with fractions 1/32, 1/16, 3/32, 1/8, 1/4 involving an arbitrary number of branes, as well as their associated geometries.