Eight-dimensional quantum Hall effect and "Octonions".
We construct a generalization of the quantum Hall effect where particles move in an eight-dimensional space under an SO(8) gauge field. The underlying mathematics of this particle liquid is that of the last normed division algebra, the octonions. Two fundamentally different liquids with distinct configuration spaces can be constructed, depending on whether the particles carry spinor or vector SO(8) quantum numbers. One of the liquids lives on a 20-dimensional manifold with an internal component of SO(7) holonomy, whereas the second liquid lives on a 14-dimensional manifold with an internal component of G2 holonomy.
Bernevig
Bogdan A
BA
Department of Physics, Stanford University, Stanford, California 94305, USA.
Hu
Jiangping
J
Toumbas
Nicolaos
N
Zhang
Shou-Cheng
SC