Fermion-Number Variation for Several Coupling Schemes in an SU(N) Chiral Soliton Background

@misc{sawado2026fermionnumber,
  title = {{Fermion-Number Variation for Several Coupling Schemes in an $\mathrmSU(N)$ Chiral Soliton Background}},
  author = {Nobuyuki Sawado and Shintaro Yamamoto},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29632},
  eprint = {2610.29632},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29632},
}

TY  - UNPB
TI  - Fermion-Number Variation for Several Coupling Schemes in an SU(N) Chiral Soliton Background
AU  - Nobuyuki Sawado
AU  - Shintaro Yamamoto
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29632
UR  - https://arxiv.org/abs/2610.29632
AB  - When topological solitons are coupled to fermions, they often induce a nontrivial fermion number. In the chiral quark soliton model (CQSM), this phenomenon underlies the identification of soliton topology with baryon number. However, whether this topology--fermion-number correspondence is determined solely by soliton topology or also depends on the fermion--soliton coupling scheme remains unclear. In this paper, we investigate this question by comparing several coupling schemes to the same SU(N) chiral soliton background. To treat the corresponding Dirac Hamiltonians within a common framework, we evaluate the variation of the regularized fermion-number along a model-parameter space. For the standard chiral Yukawa coupling of the CQSM, this variation reproduces the topological charge Q associated with π_3(SU(N)). The same result is obtained for an axial-vector coupling, whereas the fermion number variation vanishes for a vector coupling, despite the nontrivial topology of the chiral soliton background. These results provide an explicit example in which soliton topology alone does not determine the fermionic response; the topology--fermion-number correspondence also depends on how the background field is coupled to fermions.
ER  -