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

Kanazawa T, Kieburg M, Verbaarschot JJM (2019)
arXiv:1904.03274.

Preprint | Englisch
 
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Abstract / Bemerkung
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($2N_{\rm f}$) $\to $ U($N_{\rm f}+k$)$\times$U($N_{\rm f}-k$). 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.
Erscheinungsjahr
2019
Zeitschriftentitel
arXiv:1904.03274
Page URI
https://pub.uni-bielefeld.de/record/2936512

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Kanazawa T, Kieburg M, Verbaarschot JJM. Random matrix approach to three-dimensional QCD with a Chern-Simons term. arXiv:1904.03274. 2019.
Kanazawa, T., Kieburg, M., & Verbaarschot, J. J. M. (2019). Random matrix approach to three-dimensional QCD with a Chern-Simons term. arXiv:1904.03274
Kanazawa, T., Kieburg, M., and Verbaarschot, J. J. M. (2019). Random matrix approach to three-dimensional QCD with a Chern-Simons term. arXiv:1904.03274.
Kanazawa, T., Kieburg, M., & Verbaarschot, J.J.M., 2019. Random matrix approach to three-dimensional QCD with a Chern-Simons term. arXiv:1904.03274.
T. Kanazawa, M. Kieburg, and J.J.M. Verbaarschot, “Random matrix approach to three-dimensional QCD with a Chern-Simons term”, arXiv:1904.03274, 2019.
Kanazawa, T., Kieburg, M., Verbaarschot, J.J.M.: Random matrix approach to three-dimensional QCD with a Chern-Simons term. arXiv:1904.03274. (2019).
Kanazawa, Takuya, Kieburg, Mario, and Verbaarschot, Jacobus J.M. “Random matrix approach to three-dimensional QCD with a Chern-Simons term”. arXiv:1904.03274 (2019).

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arXiv: 1904.03274

Inspire: 1728693

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