Octonions and supersymmetry in three dimensions

We present two N = 1 locally supersymmetric σ-models in 3D with the seven- and eight-dimensional target spaces with the reduced G2 and Spin(7) holonomies instead of the maximal SO(7) and SO(8), respectively. It turns out that particular Wess-Zumino-Novikov-Witten-like terms are possible with the octonion structure constant for these σ-models. As a by-product, we show that a new N = 7 vector multiplet also exists in 3D with non-trivial interactions with the octonion structure constant. A non-trivial solution for the interacting vectorial field is also given