Explanation of a strange bulk-edge equality

¹ Yale University, New Haven CT 06520
² University of California, Berkeley CA 94720

^a e-mail: r.shankar@yale.edu

Abstract

In the infrared limit the N-particle ground-state wavefunctions of the bulk happen to be exactly equal to the N-point space-time correlation functions for certain topological superconductors. We explain this [1], beginning with the p+ip state in D=2+1. We write Z(J), the generating function for wavefunctions, as a path Euclidean integral. Varying the chemical potential as a function of Euclidean time between weak and strong pairing states is shown to extract the wavefunction. Upon a Euclidean rotation that exchanges time and space, approximate Lorentz invariance converts the system to one with a spatial edge and Z(J) to the generator of spacetime correlation functions for the edge fields. We also provide a D=3+1 example, superfluid ³He- B, and a pwave superfluid in D=1+1. Our method works only when particle number is not conserved, as in superconductors.