Gauge theory on nonassociative spaces

摘要: We show how to do gauge theory on the octonions and other nonassociative algebras such as “quasi-R4” models proposed in string theory. use of quasialgebras obtained by cochain twist introduced previously. The this case is twisting–equivalent usual underlying classical space. give a general U(1)-Yang–Mills example for any quasialgebra full description moduli space flat connections cube Z23 hence octonions. also obtain further results about themselves; an explicit Moyal-product them quantization functions cube, characterization their invariant under Fourier transform.