• Corpus ID: 119658436

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}
}
  • John Huerta
  • Published 17 June 2011
  • Mathematics
  • arXiv: Mathematical Physics
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… 

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References

SHOWING 1-10 OF 76 REFERENCES

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

Geometric Supergravity in d = 11 and Its Hidden Supergroup

Higher-Dimensional Algebra VI: Lie 2-Algebras

The theory of Lie algebras can be categorified starting from a new notion of '2-vector space', which we define as an internal category in Vect. There is a 2- category 2Vect having these 2-vector

An invitation to higher gauge theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge

From loop groups to 2-groups

We describe an interesting relation between Lie 2-algebras, the Kac– Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where

Elliptic Cohomology: The M -theory 3-form and E 8 gauge theory

We give a precise formulation of the M-theory 3-form potential C in a fashion applicable to topologically nontrivial situations. In our model the 3-form is related to the Chern-Simons form of an E8

Supersymmetry and the Division Algebras

Introduction to Superanalysis

1. Grassmann Algebra.- 2. Superanalysis.- 3. Linear Algebra in Z2-Graded Spaces.- 4. Supermanifolds in General.- 5. Lie Superalgebras.- 1. Lie Superalgebras.- 2. Lie Supergroups.- 3. Laplace-Casimir

Supersymmetric {Yang-Mills} Theories and Division Algebras

...