Singular values of the Dirac operator at nonzero density
High Energy Physics - Lattice
2012-12-11 v1
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.
Cite
@article{arxiv.1212.2141,
title = {Singular values of the Dirac operator at nonzero density},
author = {Takuya Kanazawa and Tilo Wettig and Naoki Yamamoto},
journal= {arXiv preprint arXiv:1212.2141},
year = {2012}
}
Comments
7 pages, talk given at Lattice 2012