# Symmetry crossover protecting chirality in Dirac spectra

@article{Kanazawa2018SymmetryCP, title={Symmetry crossover protecting chirality in Dirac spectra}, author={Takuya Kanazawa and Mario Kieburg}, journal={Journal of High Energy Physics}, year={2018}, volume={2018}, pages={1-43} }

A bstractWe consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched…

## 4 Citations

### GUE-chGUE transition preserving chirality at finite matrix size

- Mathematics, PhysicsJournal of Physics A: Mathematical and Theoretical
- 2018

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…

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

- PhysicsPhysical review letters
- 2018

A random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussianunitary ensemble while preserving chiral symmetry is considered, an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but the singular value statistics rather than the complex eigenvalue statistics.

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

- PhysicsJournal of High Energy Physics
- 2019

Abstract
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(2N
f) → U(N
f + k)×U(N
f…

### Chiral random matrix theory for colorful quark-antiquark condensates

- Materials Science
- 2020

In QCD, at high density, the color-octet quark-antiquark condensate…

## References

SHOWING 1-10 OF 103 REFERENCES

### Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

- Physics
- 2008

We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of…

### GUE-chGUE transition preserving chirality at finite matrix size

- Mathematics, PhysicsJournal of Physics A: Mathematical and Theoretical
- 2018

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…

### Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition

- Mathematics
- 2011

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n + ν) × (2n + ν) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian…

### Spectral properties of the Wilson-Dirac operator and random matrix theory

- Physics
- 2013

Random Matrix Theory has been successfully applied to lattice Quantum Chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically,…

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

- PhysicsPhysical review letters
- 2018

A random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussianunitary ensemble while preserving chiral symmetry is considered, an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but the singular value statistics rather than the complex eigenvalue statistics.

### Abelian duality , confinement , and chiral symmetry breaking in QCD ( adj )

- Physics
- 2007

We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial S × R. The absence of thermal fluctuations, and the fact that quantum…

### Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions

- Physics
- 2014

A bstractWe investigate QCD with adjoint Dirac fermions on ℝ3 × S1 with generic boundary conditions for fermions along S1. By means of perturbation theory, semiclassical methods and a chiral…

### Abelian duality, confinement, and chiral-symmetry breaking in a SU(2) QCD-like theory.

- Physics
- 2008

We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial S{sup 1}xR{sup 3}. The absence of thermal fluctuations, and the fact…

### Dirac Spectra of 2-dimensional QCD-like theories

- Physics
- 2014

We analyze Dirac spectra of two-dimensional QCD like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The…