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Boundary condition and reflection anomaly in $2+1$ dimensions
by Jiunn-Wei Chen, Chang-Tse Hsieh, Ryutaro Matsudo
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Submission summary
| Authors (as registered SciPost users): | Ryutaro Matsudo |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2306.10845v3 (pdf) |
| Date accepted: | 2024-08-07 |
| Date submitted: | 2024-07-24 05:17 |
| Submitted by: | Matsudo, Ryutaro |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
1) We added Eq.~(2.9) and sentences above it to explicitly indicate the action of the reflection on a Majorana fermion field.
2) We fixed the misuse of the symbol $N_f$ below the Eq. (2.17).
3) We corrected the sentence above (3.9).
Published as SciPost Phys. 17, 068 (2024)