Dirac Spectra in Dense QCD by Takuya Kanazawa

By Takuya Kanazawa

Gaining a theoretical knowing of the houses of ultra-relativistic dense subject has been the most vital and difficult pursuits in quantum chromodynamics (QCD). during this thesis, the writer analyzes dense quark subject in QCD with gauge workforce SU(2) utilizing low-energy potent theoretical innovations and elucidates a singular connection among statistical homes of the Dirac operator spectrum at excessive baryon chemical power and a distinct category of random matrix theories. This paintings may be seen as an extension of the same correspondence among QCD and matrix versions which used to be formerly recognized just for infinitesimal chemical potentials. In destiny numerical simulations of dense subject the analytical effects pronounced listed below are anticipated to function a great tool to extract actual observables akin to the BCS hole from numerical information at the Dirac spectrum.

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At larger μ-independence of ψψ μ, however, the agreement is less impressive, because the subleading contributions ¯ 0, in ChPT are no longer negligible. Actually ψψ continues rising beyond ψψ instead of converging to it, at higher μ. Even without the sign problem it is a nontrivial challenge to investigate the high density region using lattice QCD: when μ becomes comparable to the cutoff scale ∼1/a (a: lattice spacing), the discrete nature of the lattice shows up. As the quark number density per site approaches the maximum value ∼N f Nc allowed by the Pauli principle, quarks are essentially freezed, and the theory resembles pure Yang-Mills theory.

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