Quantum Hall effect on S3, edge states and fuzzy S3/Z2 Original Research A

We analyze the Landau problem and quantum Hall effect on S3 taking a constant background field proportional to the spin connection on S3. The effective strength of the field can be tuned by changing the dimension of the representation to which the fermions belong. The effective action for the edge excitations of a quantum Hall droplet in the limit of a large number of fermions is obtained. We find that the appropriate space for many of these considerations is S2×S2, which plays a role similar to that of CP3 vis-a-vis S4. We also give a method of representing the algebra of functions on fuzzy S3/Z2 in terms of finite-dimensional matrices.