The Axial Charge in Hilbert Space and the Role in Chiral Gauge Theories
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915894758735872 |
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| author | Yamaoka, Tatsuya |
| author_facet | Yamaoka, Tatsuya |
| contents | We investigate the Hamiltonian formulation of 1+1-dimensional staggered fermions and reconstruct the vector and axial charge operators, originally identified by Arkya Chatterjee et al., within the Wilson fermion formalism. These operators commute with the Hamiltonian and reduce, in the continuum limit, to the generators of the vector and axial $\mathrm{U}(1)$ symmetries. A notable feature of the axial charge operator is that it acts locally on operators and possesses quantized eigenvalues. Its eigenstates can therefore be interpreted as fermion states with well-defined integer chirality, analogous to those in the continuum theory. This structure enables the formulation of a gauge theory in which the axial $\mathrm{U}(1)_A$ symmetry is promoted to a gauge symmetry. We construct a Hamiltonian in terms of the eigenstates of the axial charge operator, thereby preserving exact axial symmetry on the lattice while recovering vector symmetry in the continuum limit. As applications, we study the implementation of the Symmetric Mass Generation (SMG) mechanism in the 3-4-5-0 models. Our framework admits symmetry-preserving interaction terms with quantized chiral charges, although further numerical investigation is required to confirm the realization of the SMG mechanism in interacting systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_26104 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Axial Charge in Hilbert Space and the Role in Chiral Gauge Theories Yamaoka, Tatsuya High Energy Physics - Lattice We investigate the Hamiltonian formulation of 1+1-dimensional staggered fermions and reconstruct the vector and axial charge operators, originally identified by Arkya Chatterjee et al., within the Wilson fermion formalism. These operators commute with the Hamiltonian and reduce, in the continuum limit, to the generators of the vector and axial $\mathrm{U}(1)$ symmetries. A notable feature of the axial charge operator is that it acts locally on operators and possesses quantized eigenvalues. Its eigenstates can therefore be interpreted as fermion states with well-defined integer chirality, analogous to those in the continuum theory. This structure enables the formulation of a gauge theory in which the axial $\mathrm{U}(1)_A$ symmetry is promoted to a gauge symmetry. We construct a Hamiltonian in terms of the eigenstates of the axial charge operator, thereby preserving exact axial symmetry on the lattice while recovering vector symmetry in the continuum limit. As applications, we study the implementation of the Symmetric Mass Generation (SMG) mechanism in the 3-4-5-0 models. Our framework admits symmetry-preserving interaction terms with quantized chiral charges, although further numerical investigation is required to confirm the realization of the SMG mechanism in interacting systems. |
| title | The Axial Charge in Hilbert Space and the Role in Chiral Gauge Theories |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2603.26104 |