Chirality-violating condensates in QCD and their connection with zero-mode solutions of quark Dirac equations

We demonstrate that chirality-violating condensates in massless QCD arise entirely from zero-mode solutions of the Dirac equation in arbitrary gluon fields. We propose a model in which the zero-mode solutions are the ones for quarks moving in the instanton field and calculate the quark condensate magnetic susceptibilities $\chi$ of dimension three and $\kappa$ and $\xi$ of dimension five based on this model. The good correspondence of the values of $\chi$, $\kappa$, and $\xi$ obtained using this approach with the values found from the hadronic spectrum is a serious argument that instantons are the only source of chirality-violating condensates in QCD. We discuss the temperature dependence of the quark condensate and show that the phase transition corresponding to the temperature dependence $\alpha(T)$ of the quark condensate as an order parameter is a crossover-type transition.