Scrambling in Yang-Mills

Acting on operators with a bare dimension similar to N-2 the dilatation operator of U(N) 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 similar to 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 similar to rho lambda with lambda the 't Hooft coupling.

Automated summary

By utilizing the dilatation operator of U(N) N = 4 super Yang-Mills theory, a 2-local Hamiltonian acting on a graph is defined, leading to the study of scrambling and equilibration in large N Yang-Mills theory. The dynamics on a typical graph result in scrambling within a time consistent with the fast scrambling conjecture, while at weak coupling, the system exhibits a notion of equilibration with a relaxation time characterized by t similar to rho lambda with lambda as the 't Hooft coupling.