Yukawa网络中有限各向异性传播锥的重正化群锁定
Renormalization-group locking of finite anisotropic propagation cones in Yukawa networks
AI总结：
该研究探究有限图上Yukawa相互作用能否通过重正化群动力学，使初始主轴不重合的各向异性传播扇区渐近形成共同红外空间锥，推导了相关矩阵流并验证了其收缩性质。
AI中文摘要：
不同场种类可具有初始有限各向异性传播几何，其主轴未必重合。我们探究有限图上的局域Yukawa相互作用，即便驱动锁定的相互作用变为边际无关，是否仍能生成一个共同的红外空间锥。保留正定空间动能矩阵间的全部有限失配，我们推导单圈非线性矩阵流并证明其汤普森直径全局非扩张。在连通图上，持续归一化边活性将其升级为均匀有限窗口收缩，故所有相互作用扇区渐近共享一个相对传播几何。明确的两通道Pauli-Dirac Yukawa四次项补全在有限失配初始数据的开弱耦合集上实现了持续条件。四维中Yukawa耦合在红外消失，但其累积相互作用时间发散，留下具有共同空间锥的高斯端点。对可控的两平台极值类，图距离还确定了直径减小的首个非零短时阶次。因此，共同锥可由重正化群动力学集体选择，而非作为微观共同结构强加。
英文摘要：
Different field species can begin with finite anisotropic propagation geometries whose principal axes need not coincide. We ask whether local Yukawa interactions on a finite graph can nevertheless generate one common infrared spatial cone, even when the interactions that drive the locking become marginally irrelevant. Retaining the full finite mismatch between positive-definite spatial kinetic matrices, we derive the one-loop nonlinear matrix flow and show that its Thompson diameter is globally nonexpansive. On a connected graph, persistent normalized edge activity upgrades this to a uniform finite-window contraction, so all interacting sectors asymptotically share one relative propagation geometry. An explicit two-channel Pauli-Dirac Yukawa-quartic completion realizes the persistence conditions on an open weak-coupling set of finite-mismatch initial data. In four dimensions the Yukawa couplings vanish in the infrared, yet their accumulated interaction time diverges, leaving a Gaussian endpoint with a common spatial cone. For a controlled two-plateau extremal class, graph distance also fixes the first nonzero short-time order of the diameter decrease. Thus common-cone locking can emerge from renormalization-group dynamics rather than being imposed as a microscopic common structure.
