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Fermionic backreaction on kink and topological charge pumping in the sl(2) affine Toda model coupled to matter

H. Blas1 and R. Quicaño2

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Phys. Rev. D 112, 016019 – Published 21 July, 2025

DOI: https://doi.org/10.1103/s4s4-ksbn

Abstract

We explore the Faddeev-Jackiw symplectic Hamiltonian reduction of the sl(2) affine Toda model coupled to matter, which includes new parametrizations for a scalar field and a Grassmannian fermionic field. The structure of constraints and symplectic potentials primarily dictates the strong-weak dual coupling sectors of the theory, ensuring the equivalence between the Noether and topological currents. The analytical calculations encompass the fermion-kink classical solution, the excited fermion bound states localized on the kink, and the scattering states, all of which account for the fermion backreaction on the soliton. The total energy, which includes the classical fermion-soliton interaction energy, the bound-state fermion energy, and the fermion vacuum polarization energy, is determined by the topological charge of the kink. This system satisfies first-order differential equations and a chiral current conservation equation. Our results demonstrate that the excited fermion bound states and scattering states significantly alter the properties of the kink. Notably, they give rise to a pumping mechanism for the topological charge of the in-gap kink due to fermionic backreaction, as well as the appearance of kink states in the continuum.

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Phys. Rev. D 112, 016019– Published 21 July, 2025
  • Received 14 April 2025
  • Accepted 2 July 2025
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