Chiral Lagrangian and spectral sum rules for two-color QCD at high density

Kanazawa, Takuya; Wettig, Tilo; Yamamoto, Naoki

doi:10.22323/1.091.0195

Cited by 4 publications

(2 citation statements)

References 15 publications

(22 reference statements)

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“…From the explicit knowledge of the partition functions above one could in principle derive detailed sum rules for the Dirac operator eigenvalues, as was suggested in [13,43]. However, we will be able to give more detailed unquenched density correlation functions in the following section, from which such sum rules also follow.…”

Section: The Partition Function and Two Limiting Theoriesmentioning

confidence: 97%

Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

Akemann

Kanazawa

Phillips

et al. 2011

J. High Energ. Phys.

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We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential µ. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the ε-regime of chiral perturbation theory at small µ, where µ 2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and µ is unscaled. We give explicit examples for the complex, real, and imaginary eigenvalue densities including N f = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of µ.On the mathematical side our new results include an analytical formula for the spectral density of real Wishart eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.

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Section: The Partition Function and Two Limiting Theoriesmentioning

confidence: 97%

Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

Akemann

Kanazawa

Phillips

et al. 2011

J. High Energ. Phys.

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“…In earlier work [4], we have derived the low-energy effective chiral Lagrangian for µ Λ SU (2) , identified the corresponding ε-regime, and derived Leutwyler-Smilga-type sum rules for the eigenvalues of the Dirac operator. This work has been summarized at Lattice 2009 [5].…”

Section: Introductionmentioning

confidence: 99%

Exact results for two-color QCD at low and high density

Wettig¹,

Kanazawa²,

Yamamoto³

2011

Proceedings of the XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010)

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We discuss a random matrix theory that was originally constructed to describe two-color QCD at low density in the phase with a nonzero chiral condensate. With a particular choice of a parameter, the same random matrix theory also describes the high-density phase of two-color QCD. In this phase a BCS superfluid of diquark pairs is formed, and the pattern of chiral symmetry breaking is very different from that at low density. Analytical results for the spectral density obtained from this random matrix theory allow for the extraction of the BCS gap from lattice data.

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Dirac Operator in Dense QCD

Kanazawa

2012

Dirac Spectra in Dense QCD

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Chiral Lagrangian and spectral sum rules for two-color QCD at high density

Cited by 4 publications

References 15 publications

Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

Exact results for two-color QCD at low and high density

Dirac Operator in Dense QCD

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