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arXiv · 2008.12409

Scrambling in Yang-Mills

Robert de Mello Koch·Eunice Gandote·Augustine Larweh Mahu
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Abstract

Acting on operators with a bare dimension $\Delta\sim N^2$ 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 $t\sim{p\over\lambda}$ with $\lambda$ the 't Hooft coupling.

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Robert de Mello Koch, Eunice Gandote, Augustine Larweh Mahu. 2020-08-27. Scrambling in Yang-Mills. https://doi.org/10.1007/jhep01(2021)058

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