# Topology of Helium 3A and 3B

The question concerns the topology and dimensions of Helium 3A and 3B

A. The Helium 3A phase shows the same low energy excitations as those of a 2 spatial dimensional chiral p-wave superconductor --- with the half-quantum vortex in a chiral p-wave superconductor of spinful fermions (as the order parameter of A phase of 3He). The chiral p-wave superconductor is a gapped long range entangled state with topological order.

B. The Helium 3B phase shows the nature of 3 spatial dimensional topological superconductor (TSC) with time reversal symmetry $$T^2=(-1)^f$$. The TSC is a gapped short range entangled state protected by the time reversal symmetry known as symmetry protected order.

## questions

• (Why) are Helium 3A and 3B are realized in different dimensions? 2 spatial vs. 3 spatial dimensions? Should they live in the same phase diagram with the same dimensions?

• Why are Helium 3A and 3B have realized different long vs short range entanglement?