Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields
Masayasu Hasegawa
备注：
38 pages, 21 figures, and 12 tables. A contribution to the 3rd international workshop "Lattice and Functional Techniques for QCD" held with the 7th international conference "Models in Quantum Field Theory"
The effects of external magnetic fields on monopoles, spectra of the overlap Dirac operator, instantons, and the mass of the eta-prime meson are examined by conducting lattice QCD simulations. The uniform external magnetic fields are applied to gauge field configurations with $N_{f}$ = 2 + 1 flavor quarks. The bare quark masses are tuned in order to obtain the physical values of the pion mass and of the ratio $\frac{m_{s}}{m_{u, d}}$. Standard configurations and configurations with applied external magnetic fields are generated in the color confinement and deconfinement phases. The intensity of external magnetic fields varies from $e|B|$ = 0.57 to 1.14 [GeV$^{2}$]. To examine the influence of external magnetic fields on monopoles, we first calculate the monopole density, measure the lengths of the monopole loops and compare them with the absolute value of the Polyakov loops. Next, using the generated configurations, we compute the eigenvalues and eigenvectors of the overlap Dirac operator, which preserves exact chiral symmetry. To investigate how external magnetic fields affect the spectra of the overlap Dirac operator, we compute spectral densities, compare fluctuations of the eigenvalues of the overlap Dirac operator with the predictions of random matrix theory, and estimate the number of instantons and anti-instantons from the topological charges. In addition, we analyze smearing effects on these observables and chiral symmetry breaking. Finally, we calculate the decay constant of the pseudoscalar meson, the chiral condensate, and the square mass of the eta-prime meson using the eigenvalues and eigenvectors. We then extrapolate the numerical results in the chiral limit and demonstrate the effects of external magnetic fields on the extrapolation results. This article presents preliminary results.
Zero modes of Overlap fermions, instantons, and monopoles
本研究的目的是探讨瞬子、单极子与手征对称性破缺之间的关系。磁单极子是QCD中存在的重要拓扑结构，它被认为是产生色禁闭的原因。金泽大学和比萨大学的研究小组已经通过晶格模拟得出了许多支持QCD真空是对偶超导体的结果。瞬子与手征对称性破缺有关，例如在E. V. Shuryak。从数量上澄清磁单极子和瞬子之间的关系并不容易，也因为磁单极子是三维物体，而瞬子是四维的。我们生成的配置，添加一个新的创建运营商的相反的电荷的反对称反对称对。我们观察到，创建操作符只在配置中添加长的循环。然后，我们用重叠费米子作为工具，计算了这些组态中费米子零模的数目。最后，我们发现，一个正电荷-反电荷对产生一个正负手征的零模，也就是说，产生一个正负电荷的瞬子。
