Equality of Bulk Wave Functions and Edge Correlations in Some Topological Superconductors: A Spacetime Derivation

For certain systems, the N-particle ground-state wave functions of the bulk happen to be exactly equal to the N-point spacetime correlation functions at the edge, in the infrared limit. We show why this had to be so for a class of topological superconductors, beginning with the p + ip state in D = 2 + 1. Varying the chemical potential as a function of Euclidean time between weak and strong pairing states is shown to extract the wave function. Then a Euclidean rotation that exchanges time and space and approximate Lorentz invariance lead to the edge connection. This framework readily generalizes to other dimensions. We illustrate it with a D = 3 + 1 example, superfluid He-3- B, and a p-wave superfluid in D = 1 + 1. Our method works only when the particle number is not conserved, as in superconductors.