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Topological charge asymmetry in a CPN skyrmion-fermion coupled system

Yuki Amari1,2,*, Nobuyuki Sawado3,†, and Shintaro Yamamoto3,‡

  • 1Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan
  • 2Department of Physics, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan
  • 3Department of Physics and Astronomy, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan

  • *amari.yuki@keio.jp
  • †sawadoph@rs.tus.ac.jp
  • ‡shintaroyamamoto019@gmail.com
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Phys. Rev. D 113, 065015 – Published 20 March, 2026

DOI: https://doi.org/10.1103/hkk7-x1fg

Abstract

Topology plays a central role in classifying solitonic configurations in field theories, providing robustness and a nonperturbative label, the so-called topological charge Q. In soliton-fermion coupled systems, the relation between the topological charge and the number of zero modes is well established through the index theorem. However, the physical consequences of the sign of the topological charge have remained largely unexplored. In this work, we study fermions in 2+1 dimensions coupled to skyrmions with target space CPN, particularly focusing on the backreactions of the fermions and on the sign of the topological charge. We obtain the solutions in a self-consistent manner, which exhibit an asymmetry with respect to the topological charge ±Q especially in the strong coupling regimes. This asymmetry is caused by the fermionic eigenvalue problem inherent in the self-consistent formulation. Although the Lagrangian is symmetric under Q→−Q, the coupled equations for the skyrmions and anti-skyrmions become inequivalent once fermionic backreaction is taken into account. We demonstrate the mechanism in CP1 and CP2 skyrmions, but the analysis is directly extendable for the general CPN.

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Phys. Rev. D 113, 065015– Published 20 March, 2026
  • Received 2 February 2026
  • Accepted 27 February 2026
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