Gauge theory on nonassociative spaces

Details Gauge theory on nonassociative spaces Gauge theory on nonassociative spaces

2005-06-22

arxiv.org/abs/math/0506453v1

J.Math.Phys. 46 (2005) 103519

Mathematics

Quantum Algebra

24 pages latex, two .eps figures

Scientific paper

10.1063/1.2084747

We show how to do gauge theory on the octonions and other nonassociative algebras such as `fuzzy $R^4$' models proposed in string theory. We use the theory of quasialgebras obtained by cochain twist introduced previously. The gauge theory in this case is twisting-equivalent to usual gauge theory on the underlying classical space. We give a general U(1)-Yang-Mills example for any quasi-algebra and a full description of the moduli space of flat connections in this theory for the cube $Z_2^3$ and hence for the octonions. We also obtain further results about the octonions themselves; an explicit Moyal-product description of them as a nonassociative quantisation of functions on the cube, and a characterisation of their cochain twist as invariant under Fourier transform.

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