On the N=3 and N=4 superconformal holographic dictionary

This study presents comprehensive examples of osp(N|2) Chern-Simons supergravity on AdS3 for N>2. These formulations, which include the most general boundary conditions, represent extensions of previously discovered works (Ozer and Filiz in Eur Phys J C 82:472, 2022. https://doi.org/10.1140/epjc/s10052-022-10422-w) for N<3. In our work, we show that under the loosest set of boundary conditions, the asymptotic symmetry algebras consist of two copies of the osp(3|2)k and osp(4|2)k algebras. We subsequently restrict the gauge fields upon the boundary conditions to achieve supersymmetric extensions of the Brown-Henneaux boundary conditions. Based on these results, we finally find that the asymptotic symmetry algebras are two copies of the N=3 and N=4 superconformal algebras for N=(3,3) and N=(4,4) extended higher-spin supergravity theory in AdS3.