Effective Low Energy Theories and QCD Dirac Spectra

TL;DR

This paper develops an effective theory for the QCD Dirac spectrum, showing that in certain regimes, the eigenvalues follow Random Matrix Theory predictions, and explores implications for spectra at nonzero chemical potential.

Contribution

It introduces a low energy effective theory for the QCD Dirac spectrum that captures eigenvalue distributions and their relation to Random Matrix Theory, including at nonzero chemical potential.

Findings

Dirac eigenvalues follow RMT distributions in a specific domain.

Kinetic term influences the spectral density slope.

Effective theory describes quenched QCD spectra at nonzero chemical potential.

Abstract

We analyze the smallest Dirac eigenvalues by formulating an effective theory for the QCD Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according to a Random Matrix Theory with the global symmetries of the QCD partition function. The kinetic term provides information on the slope of the average spectral density of the Dirac operator. In the second half of this lecture we interpret quenched QCD Dirac spectra at nonzero chemical potential (with eigenvalues scattered in the complex plane) in terms of an effective low energy theory.