Symmetry crossover protecting chirality in Dirac spectra

Kanazawa, Takuya; Kieburg, Mario

doi:10.1007/jhep11(2018)205

Cited by 5 publications

(13 citation statements)

References 109 publications

(198 reference statements)

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“…We derived explicit formulas for these kernels by the method of skew-orthogonal polynomials. The analysis at large matrix dimension will be carried out in [37] and a summary of these results has been reported in [62], since the calculations are very technical. Inspired from physics we particularly study the hard edge in those two works and derive the corresponding non-linear σ-model which is the chiral perturbation theory in QCD.…”

Section: Discussionmentioning

confidence: 99%

GUE-chGUE transition preserving chirality at finite matrix size

Kanazawa¹,

Kieburg²

2018

J. Phys. A: Math. Theor.

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We study a random matrix model which interpolates between the singular values of the Gaussian unitary ensemble (GUE) and of the chiral Gaussian unitary ensemble (chGUE). This symmetry crossover is analogous to the one realized by the Hermitian Wilson Dirac operator in lattice QCD, but our model preserves chiral symmetry of chGUE exactly unlike the Hermitian Wilson Dirac operator. This difference has a crucial impact on the statistics of near-zero eigenvalues, though both singular value statistics build a Pfaffian point process. The model in the present work is motivated by the Dirac operator of 3d staggered fermions, 3d QCD at finite isospin chemical potential, and 4d QCD at high temperature. We calculate the spectral statistics at finite matrix dimension. For this purpose, we derive the joint probability density of the singular values, the skew-orthogonal polynomials and the kernels for the k-point correlation functions. The skew-orthogonal polynomials are constructed by the method of mixing bi-orthogonal and skew-orthogonal polynomials, which is an alternative approach to Mehta's one. We compare our results with Monte Carlo simulations and study the limits to chGUE and GUE. As a side product, we also calculate a new type of a unitary group integral.PACS numbers: 02.10. Yn,05.50.+q,11.15.Ex,11.15.Ha,: 15B52, 33C45 ‡ The authors of [20,35] did not study the pion condensate ud + du . As such, they had no source term j and thus had a decoupling of the two quarks.

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Section: Discussionmentioning

confidence: 99%

GUE-chGUE transition preserving chirality at finite matrix size

Kanazawa¹,

Kieburg²

2018

J. Phys. A: Math. Theor.

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“…One can also obtain the result (47) from the low-energy limit of the partition function given in ( 8) for k = 0. For this purpose we exploit the parameterization [78,79]…”

Section: E Partition Function At Finite and Large Nmentioning

confidence: 99%

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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“…with m j the masses of the dynamical quarks, L = ±1 the sign of the regularization ε > 0 and λ b/f the source variables for generating the level density. In the full version of this calculation [33] we consider a more general partition function where k and N f are chosen arbitrarily. In the first step we rewrite the ratio of determinants in (5) by a Gaussian integral over an N × (2k|2N f + 2k) rectangular supermatrix V .…”

Section: Arxiv:180304122v2 [Hep-th] 30 Jul 2018mentioning

confidence: 99%

“…We expect that the result (10) reproduces the leading order of the ε-expansion in QCD for the three areas of applications discussed above. In [33] we have even carried out the integral over U explicitly, which yielded either an N f × N f or an (N f + 1) × (N f + 1) Pfaffian determinant, depending on whether N f is even or odd, respectively. This Pfaffian structure was also obtained in finite N computations by us in [38].…”

Section: Arxiv:180304122v2 [Hep-th] 30 Jul 2018mentioning

confidence: 99%

Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model

Kanazawa

Kieburg

2018

Phys. Rev. Lett.

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We consider a random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble while preserving chiral symmetry. This ensemble describes flavor symmetry breaking for staggered fermions in 3D QCD as well as in 4D QCD at high temperature or in 3D QCD at a finite isospin chemical potential. Our model is an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but we consider the singular value statistics rather than the complex eigenvalue statistics. We report on exact results for the partition function and the microscopic level density of the Dirac operator in the ε regime of QCD. We compare these analytical results with Monte Carlo simulations of the matrix model.

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Symmetry crossover protecting chirality in Dirac spectra

Cited by 5 publications

References 109 publications

GUE-chGUE transition preserving chirality at finite matrix size

GUE-chGUE transition preserving chirality at finite matrix size

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

Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model

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