At nonzero density the eigenvalues of the Dirac operator move into the complex plane, while its singular values remain real and nonnegative. In QCD-like theories, the singular-value spectrum carries information on the diquark (or pionic) condensate. We have constructed low-energy effective theories in different density regimes and derived a number of exact results for the Dirac singular values, including Banks-Casher-type relations for the diquark (or pionic) condensate, Smilga-Stern-type relations for the slope of the singular-value density, and Leutwyler-Smilgatype sum rules for the inverse singular values. We also present a rigorous index theorem for non-Hermitian Dirac operators.
|Journal||Proceedings of Science|
|Publication status||Published - 2012|
|Event||30th International Symposium on Lattice Field Theory, Lattice 2012 - Cairns, Australia|
Duration: 2012 Jun 24 → 2012 Jun 29
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