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arXiv 0901.4035hep-latcond-mat.str-elhep-phhep-th
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具有非零重子密度和任意夸克质量的二维大N QCD的求解

Solving two-dimensional large-N QCD with a nonzero density of baryons and arbitrary quark mass

Barak Bringoltz

备注：
Added discussion on emerging quark-hadron continuity, fixed factor 2 in UV regularization, regularized gamma_5 condensate, and fixed plot of gamma_1 condensate. Plots are now more pretty. Added discussion of physical meaning of results, and corrected typos. 41 pages, 25 figures
发表信息：
Phys.Rev.D79:125006,2009
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摘要：

我们在重子数B为非零的情况下，对任意质量m和体积L的夸克，求解了二维大N量子色动力学。我们充分对待胶子零模式的动力学，并检查这是如何影响的结果从以前的研究B = 0和B = 1系统。对于有限密度的重子，当m> 0时，我们发现在基态中含有一个重子晶体，其期望值为具有螺旋状空间结构的ψ-bar gamma_mu psi。我们研究这些如何演变与B和看到的体积积分的PSI酒吧PSI强烈的重子密度的变化。我们将这种新兴的晶体结构与sine-Gordon晶体进行了比较，sine-Gordon晶体被认为是轻夸克的一个很好的近似，并且发现它是重夸克的一个非常好的近似。我们还计算了基态能量E作为重子数B的函数的变化方式，并发现对于足够大的密度，函数E（B）可以用自由无质量夸克的状态方程很好地描述，从而表明夸克-强子连续性。从dE（B）/dB我们计算夸克化学势μ作为B的函数，并看到重子相互排斥。μ依赖于B的方式也允许我们将我们的发现转化为巨正则系综。沿着μ轴的相结构包含一个相变，它发生在μ值等于重子质量除以N时，并且将具有完整平移对称性的μ独立相与具有自发破缺平移对称性的μ依赖相分开。最后，我们的计算证实了部分大N的江口-河合体积独立性的存在，如在Phys.Rev.D79：105021中所描述的，只有当正确对待胶子零模时才会出现。

英文摘要：

We solve two-dimensional large-N QCD in the presence of a nonzero baryon number B, and for arbitrary quark mass m and volume L. We fully treat the dynamics of the gluonic zero modes and check how this affects results from previous studies of the B=0 and B=1 systems. For a finite density of baryons, and for any m>0, we find that the ground state contains a baryon crystal with expectation values for psi-bar gamma_mu psi that have a helix-like spatial structure. We study how these evolve with B and see that the volume integral of psi-bar psi strongly changes with the baryon density. We compare this emerging crystal structure with the sine-Gordon crystal, which is expected to be a good approximation for light quarks, and find that it is a very good approximation for surprisingly heavy quarks. We also calculate the way the ground state energy E changes as a function of the baryon number B, and find that for sufficiently large densities the function E(B) is well described by the equation of state for free massless quarks, thus suggesting a quark-Hadron continuity. From dE(B)/dB we calculate the quark chemical potential mu as a function of B and see that the baryons repel each other. The way mu depends on B also allows us to translate our findings to the grand-canonical ensemble. The resulting phase structure along the mu-axis contains a phase transition that occurs at a value of mu equal to the baryon mass divided in N, and that separates a mu-independent phase with intact translation symmetry from a mu-dependent phase with spontaneously broken translation symmetry. Finally, our calculations confirm the presence of a partial large-N Eguchi-Kawai volume independence, as described in Phys.Rev.D79:105021, that arises only if one treats the gluonic zero modes correctly.

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