Singular values of the Dirac operator at nonzero density

Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto

Research output: Contribution to journalArticle

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

Original languageEnglish
Article number076
JournalProceedings of Science
VolumePart F130497
Publication statusPublished - 2012
Externally publishedYes

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operators
condensates
sum rules
eigenvalues
theorems
quantum chromodynamics
slopes
energy

ASJC Scopus subject areas

  • General

Cite this

Singular values of the Dirac operator at nonzero density. / Kanazawa, Takuya; Wettig, Tilo; Yamamoto, Naoki.

In: Proceedings of Science, Vol. Part F130497, 076, 2012.

Research output: Contribution to journalArticle

Kanazawa, Takuya ; Wettig, Tilo ; Yamamoto, Naoki. / Singular values of the Dirac operator at nonzero density. In: Proceedings of Science. 2012 ; Vol. Part F130497.
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