论文标题
五颜六色夸克 - 易夸克冷凝水的手性随机矩阵理论
Chiral random matrix theory for colorful quark-antiquark condensates
论文作者
论文摘要
In QCD at high density, the color-octet quark-antiquark condensate $\langle\overlineψγ_0(λ^A)_C (λ^A)_Fψ\rangle$ is generally nonzero and dynamically breaks the $\mathrm{SU}(3)_C\times \ Mathrm {su}（3）_l \ Times \ Mathrm {su}（3）_r $ symmetry to对角$ \ mathrm {su}（3）_v $。我们在平均场近似中评估了该冷凝物，发现它是$μδ^2 \ log（μ/δ）$的阶，其中$δ$是夸克的BCS间隙。接下来，我们提出了一种新型的非热性手性随机基质理论，描述了五颜六色的夸克 - 易夸克冷凝水的形成。我们采用显微镜大的限制，并发现三个阶段根据模型的参数而出现。它们是颜色味的锁定相，极相和正常相。我们严格地得出了Nambu-Goldstone模式的有效理论，并确定分区函数的夸克质量依赖性。
In QCD at high density, the color-octet quark-antiquark condensate $\langle\overlineψγ_0(λ^A)_C (λ^A)_Fψ\rangle$ is generally nonzero and dynamically breaks the $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times\mathrm{SU}(3)_R$ symmetry down to the diagonal $\mathrm{SU}(3)_V$. We evaluate this condensate in the mean-field approximation and find that it is of order $μΔ^2\log(μ/Δ)$ where $Δ$ is the BCS gap of quarks. Next we propose a novel non-Hermitian chiral random matrix theory that describes the formation of colorful quark-antiquark condensates. We take the microscopic large-$N$ limit and find that three phases appear depending on the parameter of the model. They are the color-flavor locked phase, the polar phase, and the normal phase. We rigorously derive the effective theory of Nambu-Goldstone modes and determine the quark-mass dependence of the partition function.
