Holographic correspondence in topological superconductors

TL;DR

This paper develops a holographic framework linking 3D topological superconductors with their 2D boundaries and 1D defect lines, deriving effective field theories that connect bulk topological invariants to boundary phenomena.

Contribution

It introduces a consistent set of effective field theories for topological superconductors across dimensions using holographic correspondence, linking bulk invariants to boundary modes.

Findings

Derived the topological field theory for 3D class DIII superconductors.

Identified the effective theory for 2D boundary superconductors.

Connected the chiral central charge to bulk winding and boundary Chern numbers.

Abstract

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.