Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 2

Division algebras and supersymmetry IV

Pages: 383 – 449

DOI: http://dx.doi.org/10.4310/ATMP.2017.v21.n2.a2

Author

John Huerta (CAMGSD, Instituto Superior Técnico, Universidade de Lisboa, Portugal)

Abstract

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 Poincaré supergroup in precisely those spacetime dimensions where the classical Green–Schwarz superstring makes sense: $3$, $4$, $6$ and $1$$0$. In this paper, we use the same technique to construct a ‘Lie $3$-supergroup’ extending the Poincaré 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.

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This work was partially supported by FQXi grant RFP2- 08-04, by the Geometry and Mathematical Physics Project (EXCL/MATGEO/ 0222/2012), and by a postdoctoral grant from the Portuguese science foundation, SFRH/BPD/92915/2013.

Published 7 July 2017