Majorana meets Coxeter: Non-Abelian Majorana Fermions and Non-Abelian Statistics

Abstract

We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The new non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.

6 pages, 4 figures, references added, published version

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• Quark-hadron continuity under rotation: Vortex continuity or boojum?
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Spontaneous Magnetization through Non-Abelian Vortex Formation in Rotating Dense Quark Matter
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Interaction-Induced Renormalization of Tunneling into Multiple Majorana End States of a Topological Superconducting Wire
• Dirac returns: non-Abelian statistics of vortices with Dirac fermions
• Non-Abelian statistics of vortices with multiple Majorana fermions
• Anisotropic Optical Response of Dense Quark Matter under Rotation: Compact Stars as Cosmic Polarizers
• Non-Abelian Alice strings in two-flavor dense QCD
• Microscopic description of axisymmetric vortices in ${}^3{P}_2$ superfluids
• Topological Defects in the Georgi-Machacek Model
• Coupling between Majorana fermions and Nambu-Goldstone bosons inside a non-Abelian vortex in dense QCD
• Topological confinement of vortices in two-flavor dense QCD
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• The effective action of a BPS Alice string
• Non-Abelian statistics of vortices with non-Abelian Dirac fermions
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Quark-Hadron Crossover with Vortices
• Chiral non-Abelian vortex molecules in dense QCD