Random matrix approach to three-dimensional QCD with a Chern-Simons term

Understand

We propose a random matrix theory for QCD in three dimensions with a Chern-Simons term at level $k$ which spontaneously breaks the flavor symmetry according to U($2N_{\rm f}$) $\to $ U($N_{\rm f}+k$)$\times$U($N_{\rm f}-k$).

• This random matrix model is obtained by adding a complex part to the action for the $k=0$ random matrix model.
• We derive the pattern of spontaneous symmetry breaking from the analytical solution of the model.
• Additionally, we obtain explicit analytical results for the spectral density and the spectral correlation functions for the Dirac operator at finite matrix dimension, that become complex.