Disorder and quantum chromodynamics - Non-linear sigma models

The statistical properties of Quantum Chromodynamics (QCD) show universal f eatures which can be modeled by random matrices. This has been established in detailed analyses of data from lattice gauge calculations. Moreover, sys tematic deviations were found which link QCD to disordered systems in conde nsed matter physics. To furnish these empirical findings with analytical ar guments, we apply and extend the methods developed in disordered systems to construct a non-linear sigma model for the spectral correlations in QCD. O ur goal is to derive connections to other low-energy effective theories, su ch as the Nambu-Jona-Lasinio model, and to chiral perturbation theory.