单极子存在时Wilson费米子的反常行为
Anomalous behavior of Wilson fermions in the presence of monopoles
AI总结：
该研究在三维紧致U(1)规范理论中，发现单极子存在时Wilson费米子的Wilson-Dirac算子不对易，导致裸Wilson质量特定符号范围内出现极小本征值，引发味对称性破缺的反常行为。
AI中文摘要：
三维紧致U(1)规范理论在固定格点规范耦合下支持有限密度的单极子。在给出单极子密度对格点规范耦合预期依赖关系的证据后，我们研究了两味两分量Wilson费米子的低能谱随裸Wilson质量的变化。实现这两味的Wilson-Dirac算子互为厄米共轭以恢复宇称不变性，且在典型连续极限下预期的两算子对易性，在所有格点规范耦合值下的单极子存在时均不成立。这导致了反常行为：在裸Wilson质量某一符号的宽范围内，我们观察到极小本征值存在的明确证据。这些本征模通常与规范场定义的单极子数量一一对应，且在格点规范耦合的渐近 regime中，这些模式的谱与主体之间存在能隙。本征值以零为中心成对出现，其中一个符号的本征值与单极子耦合，而相反符号的模式与反单极子耦合，这意味着味对称性破缺。
英文摘要：
Three dimensional compact U(1) gauge theory supports a finite density of monopoles at a fixed lattice gauge coupling. After showing evidence for the expected dependence on the lattice coupling of the density of monopoles, we study the low lying spectrum of a two flavors of two-component Wilson fermions as a function of the bare Wilson mass. The Wilson-Dirac operator that realizes the two flavors are hermitian conjugate of each other to restore parity invariance and the commutativity of the two operators expected in the typical continuum limit is not the case in the presence of monopoles for all values of the lattice gauge coupling. This results in an anomalous behavior where we see clear evidence for the presence of very small eigenvalues for a wide range of a particular sign of the bare Wilson mass. These eigenmodes are typically in one-to-one correspondence with the number of monopoles as defined by the gauge field and the spectrum associated with these modes are separated by a gap from the bulk in the asymptotic regime of the lattice gauge coupling. The eigenvalues come in pairs around zero and the eigenvalues of one sign couple to the monopoles while the modes of the opposite sign couple to the anti-monopole implying flavor symmetry breaking.
