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It is shown that gauge field configurations with higher topological charge modify the structure of the QCD vacuum, which is reflected in its dependence on the CP-violating topological phase $theta$. To explore this, topological susceptibilities and the production of axion dark matter are studied here. The former characterize the topological charge distribution and are therefore sensitive probes of the topological structure of QCD. The latter depends on the effective potential of axions, which is determined by the $theta$-dependence of QCD. The production of cold dark matter through the vacuum realignement mechanism of axions can therefore be affected by higher topological charge effects. This is discussed qualitatively in the deconfined phase at high temperatures, where a description based on a dilute gas of instantons with arbitrary topological charge is valid. As a result, topological susceptibilities exhibit a characteristic temperature dependence due to anharmonic modifications of the $theta$-dependence. Furthermore, multi-instanton effects give rise to a topological mechanism to increase the amount of axion dark matter.
APE smearing and overlap-Dirac operator are combined to filter QCD vacuum configurations. The results obtained from overlap fermions and improved 5Li cooling are compared, both of them exhibit structures of dilute liquid of instanton. Finally the ove
In the QCD sum rules for the tetraquark (molecular) states, the higher dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10
Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of topological charge
Overlap fermions implement exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects on Luescher-Weisz-type quenched
We analyze the chiral symmetries of flavored quantum chromodynamics in two dimensions and show the existence of chiral condensates within the path-integral approach. The massless and massive cases are discussed as well, for arbitrary finite and infin