Boundary condition and reflection anomaly in $2+1$ dimensions

Abstract

It is known that the $2+1$d single Majorana fermion theory has an anomaly of the reflection, which is canceled out when 16 copies of the theory are combined. Therefore, it is expected that the reflection symmetric boundary condition is impossible for one Majorana fermion, but possible for 16 Majorana fermions. In this paper, we consider a reflection symmetric boundary condition that varies at a single point, and find that there is a problem with one Majorana fermion. The problem is the absence of a corresponding outgoing wave to a specific incoming wave into the boundary, which leads to the non-conservation of the energy. For 16 Majorana fermions, it is possible to connect every incoming wave to an outgoing wave without breaking the reflection symmetry. In addition, we discuss the connection with the fermion-monopole scattering in $3+1$ dimensions.

24 pages, 2 figures

References in corpus (5)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Missing final state puzzle in the monopole-fermion scattering
• Monopole-fermion scattering and varying Fock space
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Monopoles, Scattering, and Generalized Symmetries