Boundary condition and reflection anomaly in $2+1$ dimensions
Journal
SciPost Physics
Journal Volume
17
Journal Issue
2
Start Page
068
ISSN
2542-4653
Date Issued
2024-08-26
Author(s)
Abstract
It is known that the 2 + 1d 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.
SDGs
Publisher
Stichting SciPost
Type
journal article