### Abstract

For theories with a sign problem there is no analog of the Banks-Casher relation. This is true in particular for QCD at nonzero quark chemical potential. However, for QCD-like theories without a sign problem the Banks-Casher relation can be extended to the case of complex Dirac eigenvalues. We derive such extensions for the zero-temperature, high-density limits of two-color QCD, QCD at nonzero isospin chemical potential, and adjoint QCD. In all three cases the density of the complex Dirac eigenvalues at the origin is proportional to the BCS gap squared. 31st International.

Original language | English |
---|---|

Article number | 193 |

Journal | Unknown Journal |

Volume | 29-July-2013 |

Publication status | Published - 2013 |

Externally published | Yes |

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### ASJC Scopus subject areas

- General

### Cite this

*Unknown Journal*,

*29-July-2013*, [193].

**Banks-Casher-type relations for complex Dirac Spectra.** / Kanazawa, Takuya; Wettig, Tilo; Yamamoto, Naoki.

Research output: Contribution to journal › Article

*Unknown Journal*, vol. 29-July-2013, 193.

}

TY - JOUR

T1 - Banks-Casher-type relations for complex Dirac Spectra

AU - Kanazawa, Takuya

AU - Wettig, Tilo

AU - Yamamoto, Naoki

PY - 2013

Y1 - 2013

N2 - For theories with a sign problem there is no analog of the Banks-Casher relation. This is true in particular for QCD at nonzero quark chemical potential. However, for QCD-like theories without a sign problem the Banks-Casher relation can be extended to the case of complex Dirac eigenvalues. We derive such extensions for the zero-temperature, high-density limits of two-color QCD, QCD at nonzero isospin chemical potential, and adjoint QCD. In all three cases the density of the complex Dirac eigenvalues at the origin is proportional to the BCS gap squared. 31st International.

AB - For theories with a sign problem there is no analog of the Banks-Casher relation. This is true in particular for QCD at nonzero quark chemical potential. However, for QCD-like theories without a sign problem the Banks-Casher relation can be extended to the case of complex Dirac eigenvalues. We derive such extensions for the zero-temperature, high-density limits of two-color QCD, QCD at nonzero isospin chemical potential, and adjoint QCD. In all three cases the density of the complex Dirac eigenvalues at the origin is proportional to the BCS gap squared. 31st International.

UR - http://www.scopus.com/inward/record.url?scp=84976308239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976308239&partnerID=8YFLogxK

M3 - Article

VL - 29-July-2013

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

M1 - 193

ER -