Study Of Topological Structure Of Vacuum By Lattice QCD

The notion of the gauge field topology is important for understanding QCD vacuum. The instanton liquid model (ILM) was used as a basis for developing a rather successful semiclassically-motivated phenomenology. This allows for an interesting mechanism of spontaneous chiral symmetry breaking. Because of the important role of ILM it has been checked by lattice QCD.Some properties of the overlap-Dirac operator in smooth SU(2) instantons backgrounds are studied. The results exhibit that the overlap-Dirac operator has chirality zero-modes and "Would-be Zero-modes" with local chirality, and that the low-lying eigenmodes can reflect the fluctuations of backgrounds faithfully. It suggests that the overlap-Dirac operator can be used to study the topological structure of vacuum.In order to reduce the short range fluctuations, a few APE smearing are uesed as a pretreatment of the overlap fermions. The low-lying eigenmodes with and without APE pretreatment are compared, which shows that their space-time structures are almost the same.The X-distribution of the low-lying engenmodes for Iwasaki gauge configurations with different lattice spacings are studied. There are visible peaked maxima at X≈0.75, which suggests that the low-lying eigenmodes are local chirality. Furthermore there are chirality zero-modes appear in many configurations. All these suggest that instantons maybe dominate the QCD vacuum.Then the chirality density distributions of the low-lying engenmodes are studied, which shows clear lump structures. Through the comparison of overlap fermions and improved 5Li cooling, we get that the improved 5Li cooling and the overlap fermions can generate similar structures if we adjust cooling steps. Moreover we found that if we take about 50 APE smearing steps all these three filter methods can produce similar results. These methods are different from each other significantly, which suggests that the structures thus obtained are physical.At last overlap-Dirac operator, APE smearing and improved 5Li cooling are combined to study the topological structure of vacuum. Firstly we combine the APE smearing and overlap-Dirac operator to filter the vacuum; secondly we use 5Li cooling to cool the original configurations till they exhibit similar distributions of the low-lying eigenmodes of the overlap-Dirac operator; finally we use the cooled configurations to calculate topological charge for every structure which appeared in the low-lying eigenmodes and use our criterion to identify these structures are (anti-)instantons or not. Our calculation is done on a 16³Ã—20 lattice with 8 gauge configurations generated with Iwasaki gauge action atβ=2.746 (spacing a=0.08 fm). We obtain the results that for every configuration the total topological charge near an integer and is consistent with the number of zero modes, which are consistent with ILM; that the mean density of instantons is 1.23fm^-4 and their mean radius isρ≈0.39fm, which suggests that the liquid of instantons dominates topological charge fluctuations in quenched lattice QCD.