Singular values of the Dirac operator at nonzero density

2012/12/10 by Takuya Kanazawa, Kanazawa, Takuya, Tilo Wettig +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #hep-lat

paper · pdf · doi:10.48550/arxiv.1212.2141

7 pages, talk given at Lattice 2012

arxiv created 2012/12/10 · arxiv updated 2012/12/11

Abstract

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-Smilga-type sum rules for the inverse singular values. We also present a rigorous index theorem for non-Hermitian Dirac operators.

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