Equality of bulk wave functions and edge correlations in topological superconductors: A spacetime derivation

Abstract

For certain systems, the N-particle ground-state wavefunctions of the bulk happen to be exactly equal to the N-point space-time 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 wavefunction. Then a Euclidean rotation that exchanges time and space and approximate Lorentz invariance lead to the edge connection. We illustrate straightforward extension to other dimensions (eg. 3He- B phase in D=3+1) and to correlated states like fractionalized topological superconductors.