Heavy-tailed chiral random matrix theory

Kanazawa, Takuya

doi:10.1007/jhep05(2016)166

Cited by 5 publications

(9 citation statements)

References 74 publications

(123 reference statements)

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“…As can be seen from Figure 4 for the quenched spectral density at k = 0, in contrast to the standard GUE, the oscillatory structure of the spectral density due to peaks of individual eigenvalues is not present even for small N . This feature was also seen in other one-parameter-reweighted ensembles [70,71]. We expect that this feature will carry over to three-dimensional QCD as well.…”

Section: When Additionally Shiftingsupporting

confidence: 57%

Random matrix approach to three-dimensional QCD with a Chern-Simons term

Kanazawa

Kieburg

Verbaarschot

2019

J. High Energ. Phys.

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We propose a random matrix theory for QCD in three dimensions with a Chern-Simons term at level k which spontaneously breaks the flavor symmetry according to U. This random matrix model is obtained by adding a complex part to the action for the k = 0 random matrix model. We derive the pattern of spontaneous symmetry breaking from the analytical solution of the model. Additionally, we obtain explicit analytical results for the spectral density and the spectral correlation functions for the Dirac operator at finite matrix dimension, that become complex. In the microscopic domain where the matrix size tends to infinity, they are expected to be universal, and give an exact analytical prediction to the spectral properties of the Dirac operator in the presence of a Chern-Simons term. Here, we calculate the microscopic spectral density. It shows exponentially large (complex) oscillations which cancel the phase of the k = 0 theory. arXiv:1904.03274v1 [hep-th] 5 Apr 2019 8 The relation between the number of flavorsÑ f in [47]) and our choice N f isÑ f = 2N f . 9 Matrix models having a similar structure were studied in [68][69][70][71].

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Section: When Additionally Shiftingsupporting

confidence: 57%

Random matrix approach to three-dimensional QCD with a Chern-Simons term

Kanazawa

Kieburg

Verbaarschot

2019

J. High Energ. Phys.

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“…However the qualitative difference between the present work and [7] must be underlined. The matrix model in [7] is heavy tailed, and has no explicit color structure in the Dirac operator. By contrast, the random matrices in this paper obey Gaussian distributions, and there is an explicit color structure in the Dirac operator (22).…”

Section: So(3)mentioning

confidence: 53%

“…This type of mass term also arises in a chiral RMT discussed in [7]. However the qualitative difference between the present work and [7] must be underlined.…”

Section: So(3)mentioning

confidence: 56%

“…This type of mass term also arises in a chiral RMT discussed in [7]. However the qualitative difference between the present work and [7] must be underlined. The matrix model in [7] is heavy tailed, and has no explicit color structure in the Dirac operator.…”

Section: So(3)mentioning

confidence: 56%

“…It plays an important role in the QCD sum rule. In 1998, Stern pointed out a theoretical possibility that ψψ = 0 and chiral symmetry is instead broken by a four-quark condensate [3,4] (see also [5][6][7][8]). This interesting scenario was later ruled out by exact QCD inequalities [9] at zero chemical potential and by the 't Hooft anomaly matching condition [10] at nonzero chemical potential and zero temperature.…”

Section: Introductionmentioning

confidence: 99%

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Chiral random matrix theory for colorful quark-antiquark condensates

Kanazawa

2020

Phys. Rev. D

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In QCD at high density, the color-octet quark-antiquark condensate ψγ0(λ A )C (λ A )F ψ is generally nonzero and dynamically breaks the SU(3)C ×SU(3)L ×SU(3)R symmetry down to the diagonal SU(3)V . We evaluate this condensate in the mean-field approximation and find that it is of order µ∆ 2 log(µ/∆) where ∆ is the BCS gap of quarks. Next we propose a novel non-Hermitian chiral random matrix theory that describes the formation of colorful quark-antiquark condensates. We take the microscopic large-N limit and find that three phases appear depending on the parameter of the model. They are the color-flavor locked phase, the polar phase, and the normal phase. We rigorously derive the effective theory of Nambu-Goldstone modes and determine the quark-mass dependence of the partition function.

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Local tail statistics of heavy-tailed random matrix ensembles with unitary invariance

Kieburg¹,

Monteleone²

2021

J. Phys. A: Math. Theor.

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We study heavy-tailed Hermitian random matrices that are unitarily invariant. The invariance implies that the eigenvalue and eigenvector statistics are decoupled. The motivating question has been whether a freely stable random matrix has stable eigenvalue statistics for the largest eigenvalues in the tail. We investigate this question through the use of both numerical and analytical means, the latter of which makes use of the supersymmetry method. A surprising behaviour is uncovered in that a freely stable random matrix does not necessarily yield stable statistics and if it does then it might exhibit Poisson or Poisson-like statistics. The Poisson statistics have been already observed for heavy-tailed Wigner matrices. We conclude with two conjectures on this peculiar behaviour.

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Heavy-tailed chiral random matrix theory

Cited by 5 publications

References 74 publications

Random matrix approach to three-dimensional QCD with a Chern-Simons term

Random matrix approach to three-dimensional QCD with a Chern-Simons term

Chiral random matrix theory for colorful quark-antiquark condensates

Local tail statistics of heavy-tailed random matrix ensembles with unitary invariance

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