有限密度下QCD低能极限的超导重子管晶体
Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
摘要：
QCD的低能极限允许有限密度的超导重子管（晶体）。我们从（3+1）维的麦克斯韦规范Skyrme模型开始（这是大N展开的首阶QCD的低能极限）。我们构造了一个近似，将一个重子荷扇区中的七个耦合场方程简化为一个线性的类薛定谔方程，该方程具有一个在与管轴正交的两个空间方向上周期性的有效势（可以显式计算）。这些解表示重子超导管的有序阵列，因为（大部分）重子电荷和总能量集中在管状区域。即使在U（1）规范场为零的极限下，它们也携带一个持续的电流（消失在管外）：这样的电流不能连续变形为零，因为它与拓扑荷相连。然后，我们讨论了Skyrme模型（通常称为\mathcal{L}_{6} $, $ \mathcal{L}_{8} $等）的t Hooft展开式中的子导修正。值得注意的是，同样的方法可以在特胡夫特展开中解析地构造出任意阶的超导重子管晶体。因此，无论包含多少次引导项，这些有序规范孤子阵列都由相同的矩阵描述，并保持其主要性质，表现出普遍的特征。另一方面，子引导项可以影响的配置设置上允许的重子密度的下限的稳定性。
英文摘要：
The low energy limit of QCD admits (crystals of) superconducting Baryonic tubes at finite density. We begin with the Maxwell-gauged Skyrme model in (3+1)-dimensions (which is the low energy limit of QCD in the leading order of the large N expansion). We construct an ansatz able to reduce the seven coupled field equations in a sector of high Baryonic charge to just one linear Schrodinger-like equation with an effective potential (which can be computed explicitly) periodic in the two spatial directions orthogonal to the axis of the tubes. The solutions represent ordered arrays of Baryonic superconducting tubes as (most of) the Baryonic charge and total energy is concentrated in the tube-shaped regions. They carry a persistent current (which vanishes outside the tubes) even in the limit of vanishing U(1) gauge field: such a current cannot be deformed continuously to zero as it is tied to the topological charge. Then, we discuss the subleading corrections in the 't Hooft expansion to the Skyrme model (called usually \mathcal{L}_{6}$, $\mathcal{L}_{8}$ and so on). Remarkably, the very same ansatz allows to construct analytically these crystals of superconducting Baryonic tubes at any order in the 't Hooft expansion. Thus, no matter how many subleading terms are included, these ordered arrays of gauged solitons are described by the same ansatz and keep their main properties manifesting a universal character. On the other hand, the subleading terms can affect the stability properties of the configurations setting lower bounds on the allowed Baryon density.
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