Effective response theory for zero energy Majorana bound states in three spatial dimensions

TL;DR

This paper develops a gravitational response theory for Majorana zero modes bound to point defects in three-dimensional superconductors, revealing their non-Abelian nature and angular momentum properties through a higher-dimensional coupling approach.

Contribution

It introduces a novel gravitational response framework starting from 4+1 dimensions to describe Majorana zero modes in 3+1D superconductors, highlighting their non-Abelian characteristics.

Findings

Identifies a gravitational coupling that encodes Majorana zero modes.

Shows the emergence of an $SU(2)_2$ Kac-Moody algebra along defect lines.

Reveals angular momentum density distribution in the bulk.

Abstract

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk defect texture with the gravitational field is introduced. Diffeomorphism invariance then leads to an $SU(2)_2$ Kac-Moody current running along the defect line. The $SU(2)_2$ Kac-Moody algebra accounts for the non-Abelian nature of the zero modes in 3+1 dimensions. It is then shown to also encode the angular momentum density which permeates throughout the bulk between hedgehog-anti-hedgehog pairs.