论文标题
在阳米尔爬上
Scrambling in Yang-Mills
论文作者
论文摘要
用裸露的尺寸$δ\ sim n^2 $代表$ u（n）$ $ {\ cal n} = 4 $ super yang-mills理论的扩张操作员定义了2个局部汉密尔顿的表演。自由度与图形的顶点有关，而边缘对应于哈密顿量中的术语。该图具有$ p \ sim n $顶点。使用这种哈密顿量，我们研究了大型$ yang-mills理论中的争夺和平衡。我们表征了典型的图，因此是典型的哈密顿量。对于典型的图，动力学会导致在与快速争夺猜想一致的时间内争夺。此外，该系统在薄弱的耦合上表现出与放松时间的平衡概念，由$ t \ sim {p \overλ} $给出，$λ$ the thooft耦合。
Acting on operators with a bare dimension $Δ\sim N^2$ the dilatation operator of $U(N)$ ${\cal N}=4$ super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has $p\sim N$ vertices. Using this Hamiltonian, we study scrambling and equilibration in the large $N$ Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by $t\sim{p\overλ}$ with $λ$ the 't Hooft coupling.
