Download Dirac Spectra in Dense QCD by Takuya Kanazawa PDF

By Takuya Kanazawa

Gaining a theoretical knowing of the homes of ultra-relativistic dense subject has been essentially the most very important and demanding objectives in quantum chromodynamics (QCD). during this thesis, the writer analyzes dense quark subject in QCD with gauge team SU(2) utilizing low-energy powerful theoretical options and elucidates a unique connection among statistical houses of the Dirac operator spectrum at excessive baryon chemical power and a distinct category of random matrix theories. This paintings might be seen as an extension of the same correspondence among QCD and matrix versions which was once formerly identified just for infinitesimal chemical potentials. In destiny numerical simulations of dense topic the analytical effects said listed below are anticipated to function a great tool to extract actual observables reminiscent of the BCS hole from numerical info at the Dirac spectrum.

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The valence quark mass [211]. On the other hand, the replica trick [216, 217] is technically simpler but is known to give exact results in the ε-regime only when it is combined with the Toda lattice equation [218, 219]. While it reveals the meaning of the ChRMT partition function as a τ -function of the Toda hierarchy, it leaves much to be desired, at least in two aspects. First, it is shown to work only for β = 2. The relevance of the Pfaff hierarchy to β = 1 and 4 is conjectured [220–223], but remains to be clarified.

While the microscopic spectral correlation functions are verified to reproduce the Leutwyler-Smilga sum rules, the converse is not true. It was explicitly shown by Verbaarschot using ChRMT [187] that different spectral densities satisfy identical spectral sum rules for N f = 1 [187]. Another counter-example occurs in QCD with nonzero chemical potential, which will be reviewed later. The bottom line is that we must introduce bosonic quarks in order to derive not only sum rules but also the full spectral correlation functions.

Based on symmetry arguments, one can write down the leading-order effective Lagrangian at μ = 0, with both the mass term and the diquark source, as L= F2 tr[∂μ 2 † ∂μ ] + mG Re tr[I2N f ] + j G Re tr i IN f 0 0 i IN f The Gell-Mann−Oaks−Renner relation is obtained by expanding second order as m2 + j 2 G , m 2π = F2 where G ≡ ¯ 0| | ψψ ¯ with ψψ 2N f 0 . 25) around I2N f to the chiral condensate at m = μ = 0. 2 Two-Color QCD at Low Density 21 In three-color QCD, ChPT does not explicitly depend on μ, since the pions ¯ 5 ψ carry no baryon charge.

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