2025/02/19 by Suzuki, Tsuneo
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2502.13434
When Abelian monopoles due to violation of the non-Abelian Bianchi identity Jμ(x) condense in the vacuum, color confinement of QCD is realized by the Abelian dual Meissner effect. Moreover VNABI affects also topological features of QCD drastically. Firstly, self-dual instantons can not be a classical solution of QCD. Secondly, the topological charge density is not expressed by a total derivative of the Chern-Simons density Kμ(x), but has an additional term L(x)=2Tr(Jμ(x)Aμ(x)). Thirdly, the axial U(1) anomaly is similarly modified, while keeping the Atiyah-Singer index theorem unchanged. However, unless the integrated additional term χ=(g2/16π2)∫ d4xL(x) is not zero, these modified relations are not compatible with gauge invariance. The additional term χis evaluated in the framework of Monte-Carlo simulations on SU(2) lattices in details with partial gauge fixings such as the Maximal Center gauge (MCG). The term χis largely fluctuating around zero before the gradient flow and tends to vanish after small gradient flow time (τ). The bosonic definition of the topological charge Qt and its Abelian counterpart Qa written by Abelian field strengths are measured also on the lattices. When χis zero, Qa=3Qt is expected theoretically, but a simple lattice definition of Qa is fluctuating between -2 and -3 in MCG, when Qt is stabilized around -1.