Minimal area surfaces dual to Wilson loops and the Mathieu equation

@article{Huang2016MinimalAS,
  title={Minimal area surfaces dual to Wilson loops and the Mathieu equation},
  author={Changyu Huang and Yifei He and Martin Kruczenski},
  journal={Journal of High Energy Physics},
  year={2016},
  volume={2016},
  pages={1-26}
}
A bstractThe AdS/CFT correspondence relates Wilson loops in N=4$$ \mathcal{N}=4 $$ SYM to minimal area surfaces in AdS5× S5 space. Recently, a new approach to study minimal area surfaces in AdS3 ⊂ AdS5 was discussed based on a Schroedinger equation with a periodic potential determined by the Schwarzian derivative of the shape of the Wilson loop. Here we use the Mathieu equation, a standard example of a periodic potential, to obtain a class of Wilson loops such that the area of the dual minimal… 

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