非零化学势非猝灭双色QCD的随机矩阵理论
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
摘要：
我们解决了一个随机的两个矩阵模型与两个真正的非对称矩阵，其主要目的是描述某些方面的量子色动力学与两种颜色和动力学费米子在非零夸克化学势μ。在这个对称类中，狄拉克算子的行列式是实数，但不一定是正数。尽管存在这个符号问题，但未猝灭的矩阵模型仍然是完全可解的，并在两种不同的物理场景/极限下提供了狄拉克算符谱的详细预测：（i）手征微扰理论在小μ时的ε区域，其中μ ^2乘以体积在无限体积极限下保持固定;（ii）高密度区域，其中形成BCS间隙，μ未标度。我们给出了明确的例子，复杂的，真正的，和虚特征值密度，包括Nf=2非退化的味道。虽然两个退化的群众的极限没有符号的问题，可以用标准的晶格技术进行测试，我们分析的严重性的符号问题的非退化的群众作为一个函数的质量分裂和亩。在数学方面，我们的新结果包括一个分析公式的频谱密度的实Wishart本征值的极限（i）的弱非厄米性，从而完成了以前的解决方案，相应的淬火模型的两个真正的非对称Wishart矩阵。
英文摘要：
We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the epsilon-regime of chiral perturbation theory at small mu, where mu^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and mu is unscaled. We give explicit examples for the complex, real, and imaginary eigenvalue densities including Nf=2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of mu. On the mathematical side our new results include an analytical formula for the spectral density of real Wishart eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.
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