AI 中文总结
该研究提出具有精确格手征对称性的费米子Villain模型，耦合Villain玻色子与Kitaev链以规避无-go定理，实现U(1)对称性，解析证明对称质量生成，计算格Schwinger模型等质量谱并与连续统结果吻合。
AI 中文摘要
我们提出了一种费米性格点哈密顿量，其能精确实现1+1维无质量狄拉克费米子的U(1)ₗ×U(1)ᵣ整体对称性及相关手征反常。该构造将Villain玻色子与Majorana费米子的Kitaev链耦合，其中玻色场是规避Nielsen-Ninomiya型无-go定理的关键。对于该模型的两个副本，我们实现了无反常的U(1)₃₄₅₀整体对称性并构造了对称边界条件。我们通过费米T对偶将保对称的六费米子相互作用映射为费米双线性项，解析证明了对称质量生成。最后，通过规范一般无反常整体对称性，我们得到了一大类格手征规范理论。作为非平凡应用，我们计算了格Schwinger模型和3450规范理论的质量谱，发现其与对应的连续统结果一致。
英文摘要
We present a fermionic lattice Hamiltonian that exactly realizes the $\mathrm{U(1)}_\mathrm{L}\times \mathrm{U(1)}_\mathrm{R}$ global symmetry and the associated chiral anomalies of a massless Dirac fermion in 1+1 dimensions. The construction couples Villain bosons to a Kitaev chain of Majorana fermions, where the bosonic fields are essential for evading Nielsen-Ninomiya-type no-go theorems. For two copies of our model, we realize the anomaly-free $\mathrm{U(1)}_{3450}$ global symmetry and construct symmetric boundary conditions. We analytically demonstrate symmetric mass generation by mapping the symmetry-preserving six-fermion interactions to fermion bilinear terms using fermionic T-duality. Finally, by gauging general anomaly-free global symmetries, we obtain a broad class of lattice chiral gauge theories. As nontrivial applications, we compute the mass spectra of the lattice Schwinger model and the 3450 gauge theory, finding agreement with the corresponding continuum results.
Comments12 pages
