Integrable systems and the boundary dynamics of higher spin gravity on AdS3

@article{Ojeda2020IntegrableSA,
  title={Integrable systems and the boundary dynamics of higher spin gravity on AdS3},
  author={Emilio Ojeda and Alfredo P'erez},
  journal={arXiv: High Energy Physics - Theory},
  year={2020}
}
We introduce a new set of boundary conditions for three-dimensional higher spin gravity with gauge group $SL(3,\mathbb{R})\times SL(3,\mathbb{R})$, where its dynamics at the boundary is described by the members of the modified Boussinesq integrable hierarchy. In the asymptotic region the gauge fields are written in the diagonal gauge, where the excitations go along the generators of the Cartan subalgebra of $sl(3,\mathbb{R})\oplus sl(3,\mathbb{R})$. We show that the entire integrable structure… 
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