Dirac Spectra in Dense QCD

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Takuya Kanazawa

   Pages 1-6

3. QCD with Chemical Potential and Matrix Models

   • Takuya Kanazawa

   Pages 7-50

4. Dirac Operator in Dense QCD

   • Takuya Kanazawa

   Pages 51-99

5. Three-fold Way at High Density

   • Takuya Kanazawa

   Pages 101-121

6. Conclusions

   • Takuya Kanazawa

   Pages 123-125

7. Back Matter

   Pages 127-136

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Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.

• BCS Gap
• Chiral Perturbation Theory
• Chiral Random Matrix Theory
• Large-N Limit of Strong Non-Hermiticity
• Leutwyler-Smilga Spectral Sum Rules
• Microscopic Spectral Density
• QCD Thesis
• QCD-like Theories at High Density
• Two-color QCD

• , Department of Physics, University of Regensburg, Regensburg, Germany

  Takuya Kanazawa

Dr. Takuya Kanazawa
Department of Physics
University of Regensburg
Universitätsstraße 31
93053 Regensburg
Deutschland/Germany

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