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

• Published in: The journal of high energy physics Vol. 2019; no. 10; pp. 1 - 41
• Main Authors: Kanazawa, Takuya, Kieburg, Mario, Verbaarschot, Jacobus J. M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Broken symmetry; Chern-Simons Theories; Chiral Lagrangians; Classical and Quantum Gravitation; Density; Elementary Particles; Exact solutions; Field Theories in Lower Dimensions; Flavor (particle physics); High energy physics; Mathematical analysis; Matrix methods; Matrix Models; Matrix theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spectra; Spectral correlation; String Theory; Field Theories in Lower Dimensions; Chiral Lagrangians; Chern-Simons Theories; Matrix Models
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2019)074

A bstract 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(2 N f ) → U( N f + k ) × U( N 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 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.