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

  • Takuya KanazawaEmail author
  • Mario Kieburg
  • Jacobus J. M. Verbaarschot
Open Access
Regular Article - Theoretical Physics


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(2Nf) U(Nf + k)×U(Nf− 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 func- tions for the Dirac operator at finite matrix dimension, that become complex. In the micro- scopic 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.


Matrix Models Chern-Simons Theories Chiral Lagrangians Field Theories in Lower Dimensions 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Takuya Kanazawa
    • 1
    Email author
  • Mario Kieburg
    • 2
  • Jacobus J. M. Verbaarschot
    • 3
  1. 1.Research and Development GroupHitachi, Ltd.TokyoJapan
  2. 2.School of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia
  3. 3.Department of Physics and AstronomyStony Brook UniversityStony BrookU.S.A.

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