Bosonization with a background $U(1)$ gauge field

Abstract

Bosonization is one of the most significant frameworks to analyze fermionic systems. In this work, we propose a new bosonization of Dirac fermion coupled with $U(1)$ background gauge field consistent with gauge invariance, global chiral anomaly matching and fermion-boson operator correspondence, either of which is not satisfied by previously developed bosonizations. The bilinear Dirac-mass term condensation paradox and its generalized form are resolved by our bosonization. This new bosonization approach to interacting systems also correctly captures the conformal characters of a significant class of critical lattice models, such as conformal dimensions and conformal anomaly of XXZ spin chain with twisted boundary condition. Our work clarifies the equivalence of fermionic flux insertion and bosonic background charge insertion for two-dimensional conformal field theory.

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References in corpus (7)

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• Generalized Global Symmetries
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
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Cited by in corpus (8)

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• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model