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arXiv · 2606.07955

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

L. Haddad·K. Gonzales·J. Kahanek·M. Kolding·J. Maguire·V. Palombi·H. Truelson
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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 $\mathfrak{sl}(2,\mathbb{R})$ 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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L. Haddad, K. Gonzales, J. Kahanek, M. Kolding, J. Maguire, V. Palombi, H. Truelson. 2026-06-06. Spin-charge deconfinement from a self-consistent dressing of Fierz-complete $(1+1)$d Dirac fermions. https://arxiv.org/abs/2606.07955

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