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

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.

arXiv comment7 pages, 3 figures

References in corpus (24)

• Topological Insulators
• Topological insulators and superconductors
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
• Gravitational Anomalies and Thermal Hall effect in Topological Insulators
• Majorana Fermions and Non-Abelian Statistics in Three Dimensions
• Torsional Response and Dissipationless Viscosity in Topological Insulators
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Axion topological field theory of topological superconductors
• Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions
• Weakly-Coupled non-Abelian Anyons in Three Dimensions
• Non-Abelian statistics versus the Witten anomaly
• Identifying non-Abelian topological ordered state and transition by momentum polarization

Cited by in corpus (4)

• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Four-band non-Abelian topological insulator and its experimental realization
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Nested Defects on the Boundary of Topological Superconductors