Chiral fermions in lattice QCD and random matrix theory

Abstract

In this thesis I present numerical results from quantum chromodynamics with chiral fermions in the quenched approximation. In particular, the thesis is divided into three topics: 1) We investigated the chiral phase transition in the complex and real sector of the Polyakov loop separately. Despite claims in the literature we have found no dependence of the critical temperature of the chiral phase transition on the Polyakov loop sector. 2) Calorons are supposed to be responsible for the spontaneous breaking of the chiral symmetry. We found evidence for caloron states on the lattice by looking at the localization properties of the low-lying eigenmodes of the Dirac operator. 3) Normal modes represent a specific basis of the probability density of the Dirac eigenvalues in chiral random matrix theory. We have compared numerical data from lattice QCD to predictions of chiral random matrix theory and found good agreement