# Division Algebras, Supersymmetry and Higher Gauge Theory

@article{Huerta2011DivisionAS, title={Division Algebras, Supersymmetry and Higher Gauge Theory}, author={John Huerta}, journal={arXiv: Mathematical Physics}, year={2011} }

From the four normed division algebras--the real numbers, complex numbers, quaternions and octonions, of dimension k=1, 2, 4 and 8, respectively--a systematic procedure gives a 3-cocycle on the Poincare superalgebra in dimensions k+2=3, 4, 6 and 10, and a 4-cocycle on the Poincare superalgebra in dimensions k+3=4, 5, 7 and 11. The existence of these cocycles follow from spinor identities that hold only in these dimensions, and which are closely related to the existence of the superstring in…

## 22 Citations

### Division Algebras and Supersymmetry IV

- Mathematics
- 2011

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…

### Higher geometric prequantum theory and The Brane

- Mathematics
- 2013

Higher brane GS-WZW actions and Noether super Lie n-algebras from higher super-orbispaces Contents 1 Motivation: The localized WZW σ-model 2 2 Example I: Some super p-brane σ-models 3 3 Boundary…

### The higher-algebraic skeleton of the superstring -- a case study

- Physics, Mathematics
- 2021

A novel Lie-superalgebraic description of the superstring in the super-Minkowskian background is extracted from the Cartan-Eilenberg super-1-gerbe geometrising the higher gauge field (the…

### Equivariant Cartan-Eilenberg supergerbes for the Green-Schwarz superbranes I. The super-Minkowskian case

- Mathematics
- 2017

An explicit gerbe-theoretic description of the super-$\sigma$-models of the Green-Schwarz type is proposed and its fundamental structural properties, such as equivariance with respect to…

### M-theory from the superpoint

- MathematicsLetters in Mathematical Physics
- 2018

The “brane scan” classifies consistent Green–Schwarz strings and membranes in terms of the invariant cocycles on super Minkowski spacetimes. The “brane bouquet” generalizes this by consecutively…

### M-theory from the superpoint

- MathematicsLetters in Mathematical Physics
- 2018

The “brane scan” classifies consistent Green–Schwarz strings and membranes in terms of the invariant cocycles on super Minkowski spacetimes. The “brane bouquet” generalizes this by consecutively…

### A higher Chern-Weil derivation of AKSZ sigma-models

- Mathematics
- 2013

Chern–Weil theory provides for each invariant polynomial on a Lie algebra 𝔤 a map from 𝔤-connections to differential cocycles whose volume holonomy is the corresponding Chern–Simons theory action…

### Super-Lie n-algebra extensions, higher WZW models and super-p-branes with tensor multiplet fields

- Mathematics
- 2013

We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory…

### Teleparallel Gravity as a Higher Gauge Theory

- Mathematics
- 2015

We show that general relativity can be viewed as a higher gauge theory involving a categorical group, or 2-group, called the teleparallel 2-group. On any semi-Riemannian manifold M, we first…

### Equivariant Cartan-Eilenberg supergerbes II. Equivariance in the super-Minkowskian setting

- Mathematics
- 2019

This is a continuation of a programme, initiated in Part I [arXiv:1706.05682], of geometrisation, compatible with the SUSY present, of the Green-Schwarz $(p+2)$-cocycles coupling to the topological…

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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…

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