Paper detail

Division Algebras and Supersymmetry IV

Recent work applying higher gauge theory to the superstring has indicated the presence of 'higher symmetry', and the same methods work for the super-2-brane. In the previous paper in this series, we used a geometric technique to construct a 'Lie 2-supergroup' extending the Poincare supergroup in precisely those spacetime dimensions where the classical Green-Schwarz superstring makes sense: 3, 4, 6 and 10. In this paper, we use the same technique to construct a 'Lie 3-supergroup' extending the Poincare supergroup in precisely those spacetime dimensions where the classical Green-Schwarz super-2-brane makes sense: 4, 5, 7 and 11. Because the geometric tools are identical, our focus here is on the precise definition of a Lie 3-supergroup.