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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…
The Algebra of Grand Unified Theories
The Standard Model is the best tested and most widely accepted theory of elementary particles we have today. It may seem complicated and arbitrary, but it has hidden patterns that are revealed by the…
Division Algebras and Supersymmetry I
Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10.…
The strangest numbers in string theory.
How a forgotten number system invented in the 19th century, called octonions, may provide the simplest explanation for why the universe could have ten dimensions is reported.
Division Algebras, Supersymmetry and Higher Gauge Theory
- J. Huerta
- 17 June 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…
Division Algebras and Supersymmetry IV
- J. Huerta
- 17 March 2010
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…
M-theory from the superpoint
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…
How Space‐Times Emerge from the Superpoint
- J. Huerta
- PhysicsFortschritte der Physik
- 7 March 2019
We describe how the super Minkowski space‐times relevant to string theory and M‐theory, complete with their Lorentz metrics and spin structures, emerge from a much more elementary object: the…
G2 and the Rolling Ball
Understanding the exceptional Lie groups as the symmetry groups of simpler objects is a long-standing program in mathematics. Here, we explore one famous realization of the smallest exceptional Lie…
The Magic Square of Lie Groups: The 2 × 2 Case
A unified treatment of the 2 × 2 analog of the Freudenthal–Tits magic square of Lie groups is given, providing an explicit representation in terms of matrix groups over composition algebras.