Abstract
We study nonlinear dynamics of the flux tube between an external quark-antiquark pair in $$ +AFw-mathcal{N} = 4 $$ super Yang-Mills theory using the AdS/CFT duality. In the gravity side, the flux tube is realized by a fundamental string whose endpoints are attached to the AdS boundary. We perturb the endpoints in various ways and numerically compute the time evolution of the nonlinearly oscillating string. As a result, cusps can form on the string, accompanied by weak turbulence and power law behavior in the energy spectrum. When cusps traveling on the string reach the boundary, we observe the divergence of the force between the quark and antiquark. Minimal amplitude of the perturbation below which cusps do not form is also investigated. No cusp formation is found when the string moves in all four AdS space directions, and in this case an inverse energy cascade follows a direct cascade.
Highlights
The gauge/gravity duality [1,2,3] is successfully applied to investigating strongly coupled gauge theories
As a phenomena characteristic in non-linear dynamics, it has been found that long time evolution of the D7-brane generates a singularity on the brane, and this is understood from the viewpoint of weak turbulence on the D7-brane: the energy in the spectrum is transferred from large to small scales [10,11,12]
We monitor the roots of JI, which typically appear as curves on the (u, v)-plane. If these curves overlap at a point, we find cusp formation, and if the overlap continues in the time evolution, it is implied that the cusps continue to exist
Summary
The gauge/gravity duality [1,2,3] is successfully applied to investigating strongly coupled gauge theories. To gain a deep insight into this kind of nonlinear dynamics in the gauge/gravity duality, in this paper, we will consider a string in AdS dual to the flux tube between a quark-antiquark pair in N = 4 super Yang-Mills theory, and fully solve its nonlinear time evolution with a help of numerical techniques. This setup corresponds to focusing on a Yang-Mills flux tube compared with the collective mesons described in the D3/D7 system. We explain details for the numerical computations and derive some formulae used in the main text
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