2014/09/15 by John Huerta, Huerta, John
Physics and Astronomy · #Black Holes and Theoretical Physics #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1409.4361
openalex publication_date 2014/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.