Lattice calculation of point-to-point Hadron current correlation functions in the QCD vacuum

Instanton-dyon ensembles reproduce deconfinement and chiral restoration phase transitions

Paradigm shift in gauge topology at finite temperatures, from the instantons to their constituents – instanton-dyons – has recently lead to studies of their ensembles and very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at suffciently high density explains the chiral symmetry breaking transition. Unlike instantons, these objects have electric and magnetic charges. Simulations of the instanton-dyon ensembles have demonstrated that their back reaction on the Polyakov line modifies its potential and generates the deconfinement phase transition. For the Nc = 2 gauge theory the transition is second order, for QCD-like theory with Nc = 2 and two light quark flavors Nf = 2 both transitions are weak crossovers at happening at about the same condition. Introduction of quark-flavor-dependent periodicity phases (imaginary chemical potentials) leads to drastic changes in both transitions. In particulaly, in the so called Z(Nc) – QCD model the deconfinement transforms to strong first order transition, while the chiral condensate does not disappear at all. The talk will also cover more detailed studies of correlations between the dyons, effective eta’ mass and other screening masses.

Evidence for instanton-induced dynamics from lattice QCD

We perform a study of the nonperturbative dynamics of the light-quark sector of QCD, based on some recent results of lattice simulations with chiral fermions. We analyze some correlators that are designed to probe the Dirac structure of the quark-quark interaction at different scales. We show that, in the nonperturbative regime, such an interaction contains very large scalar and pseudoscalar components. We observe quantitative agreement between lattice QCD results and the predictions of the instanton liquid model. Moreover, we study how the quark-quark interaction is modified, when quark loops are suppressed. We observe a dramatic effect related to the loss of unitarity, which is naturally explained in the instanton picture. Such an effect cannot be explained in a Dyson-Schwinger equations (DSE) approach, if one assumes a vector quark-gluon coupling.

Implications of the ALEPH tau-lepton decay data for perturbative and nonperturbative QCD

We use ALEPH data on hadronic tau decays in order to calculate Euclidean coordinate space correlation functions in the vector and axial-vector channels. The linear combination V-A receives no perturbative contribution and is quantitatively reproduced by the instanton liquid model. In the case of V+A the instanton calculation is in good agreement with the data once perturbative corrections are included. These corrections clearly show the evolution of alpha(s). We also analyze the range of validity of the operator product expansion (OPE). We conclude that the range of validity of the OPE is limited to x less, similar 0.3 fm, whereas the instanton model describes the data over the entire range.