Title: Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum Show Chinese title

Title: QCD 真空中的低维长程拓扑荷结构

Abstract: While sign-coherent 4-dimensional structures cannot dominate topological charge fluctuations in the QCD vacuum at all scales due to reflection positivity, it is possible that enhanced coherence exists over extended space-time regions of lower dimension. Using the overlap Dirac operator to calculate topological charge density, we present evidence for such structure in pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium configuration is dominated by two oppositely-charged sign-coherent connected structures (``sheets'') covering about 80% of space-time. Each sheet is built from elementary 3-d cubes connected through 2-d faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18% of the most intense space-time points organized into a global long-range structure, involving connected parts spreading over maximal possible distances. We find that the skeleton is locally 1-dimensional and propose that its geometrical properties might be relevant for understanding the possible role of topological charge fluctuations in the physics of chiral symmetry breaking. Show Chinese abstract

Abstract: 尽管由于反射正定性，符号一致的四维结构不能在整个尺度上主导QCD真空中的拓扑电荷涨落，但在较低维度的扩展时空区域内可能存在增强的一致性。 利用重叠Dirac算符计算拓扑电荷密度，我们在纯胶子SU(3)格点规范理论中提供了这种结构的证据。 研究发现，一个典型的平衡构型主要由两个相反电荷的符号一致且连接的结构（“薄片”）占据，这些结构覆盖了大约80%的时空区域。 每个薄片由通过二维面相连的基本三维立方体组成，并近似于嵌入四维空间中的低维弯曲流形（或者可能是分形结构）。 薄片的核心是由约18%的最强烈时空点组成的“骨架”，这些点组织成了一个全局长程结构，涉及最大可能距离上的连接部分。 我们发现骨架在局部是一维的，并提出其几何属性可能与理解拓扑电荷涨落在手征对称破缺物理中的潜在作用相关。