Vortex Fractional Fermion Number through Heat Kernel methods and Edge States

Abstract

Computing the vacuum expectation of fermion number operator on a soliton background is often challenging. A recent proposal in arXiv:2305.13606 simplifies this task by considering the soliton in a bounded region and relating the $\eta$ invariant, and thus the fermion number, to a specific heat kernel coefficient and to contributions from the edge states. We test this method in a system of charged fermions living on an Abrikosov-Nielsen-Olesen (ANO) vortex background. We show that the resulting $\eta$ invariant does not depend on boundary conditions (within a certain class), thereby supporting the validity of the method. Our analysis reveals a nontrivial feature for the fermionic spectrum in the vortex-induced Higgs phase. As a by-product, we also find that for a vortex living on a disk, the edge states carry fractional charge.

15 pages, 1 figure. v2: Details added, one reference added, matches PRD version

References in corpus (12)

• Heat kernel expansion: user's manual
• Electron fractionalization for two-dimensional Dirac fermions
• Gravitational parity anomaly with and without boundaries
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• Quantum corrections to the mass of the supersymmetric vortex
• Fermionic Vacuum Energy from a Nielsen-Olesen Vortex
• Quantum QED Flux Tubes in 2+1 and 3+1 Dimensions
• Soliton fractional charge of disordered graphene nanoribbon
• Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts
• Non-topological fractional fermion number in the Jackiw-Rossi model
• Quantum energies of BPS vortices in $D=2+1$ and $D=3+1$
• Edge states and the $\eta$ invariant