Spin-charge deconfinement from a self-consistent dressing of Fierz-complete (1+1)d Dirac fermions

Abstract

We develop a self-consistent dressing for (1+1)d Dirac fermions with Fierz-complete four-fermion interactions, extending the spin-charge formalism of~\cite{Haddad2024}. By studying the associated composite connection, we characterize obstructions to trivializing the Dirac operator and prove a trivialization theorem under which spin-charge separation, half-infinite Wilson-line dressing, and flat-connection holonomy arise as regime limits of the single dressing. In particular, the chiral-difermion transition is a deconfinement transition for the spin and charge degrees of freedom, mediated by an emergent sl(2,ℝ) gauge field and measured by a Wilson-loop area law in the chiral phase. We show that our formulation provides a realization of the conjectured Faddeev--Niemi link between spin-charge separation and confinement.

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BibTeX RIS

BibTeX

@misc{haddad2026spincharge,
  title = {{Spin-charge deconfinement from a self-consistent dressing of Fierz-complete $(1+1)$d Dirac fermions}},
  author = {L. Haddad and K. Gonzales and J. Kahanek and M. Kolding and J. Maguire and V. Palombi and H. Truelson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.07955},
  eprint = {2606.07955},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.07955},
}

RIS

TY  - UNPB
TI  - Spin-charge deconfinement from a self-consistent dressing of Fierz-complete (1+1)d Dirac fermions
AU  - L. Haddad
AU  - K. Gonzales
AU  - J. Kahanek
AU  - M. Kolding
AU  - J. Maguire
AU  - V. Palombi
AU  - H. Truelson
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2606.07955
UR  - https://arxiv.org/abs/2606.07955
AB  - We develop a self-consistent dressing for (1+1)d Dirac fermions with Fierz-complete four-fermion interactions, extending the spin-charge formalism of~\cite{Haddad2024}. By studying the associated composite connection, we characterize obstructions to trivializing the Dirac operator and prove a trivialization theorem under which spin-charge separation, half-infinite Wilson-line dressing, and flat-connection holonomy arise as regime limits of the single dressing. In particular, the chiral-difermion transition is a deconfinement transition for the spin and charge degrees of freedom, mediated by an emergent sl(2,ℝ) gauge field and measured by a Wilson-loop area law in the chiral phase. We show that our formulation provides a realization of the conjectured Faddeev--Niemi link between spin-charge separation and confinement.
ER  -

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