On the $$\mathcal {N}=3$$ N = 3 and $$\mathcal {N}=4$$ N = 4 superconformal holographic dictionary - H. T. Özer; Aytül Filiz (European Physical Journal C: Particles and Fields)
Abstract This study presents comprehensive examples of $$\mathfrak {osp}(\mathcal {N}|2)$$ osp ( N | 2 ) Chern–Simons supergravity on $$AdS_3$$ A d S 3 for $$\mathcal {N}>2$$ 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 $$\mathcal {N}<3$$ 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 $$\mathfrak {osp}(3|2)_k$$ osp ( 3 | 2 ) k and $$\mathfrak {osp}(4|2)_k$$ 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 $$\mathcal {N}=3$$ N = 3 and $$\mathcal {N}=4$$ N = 4 superconformal algebras for $$\mathcal {N}=(3,3)$$ N = ( 3 , 3 ) and $$\mathcal {N}=(4,4)$$ N = ( 4 , 4 ) extended higher-spin supergravity theory in $$AdS_3$$ A d S 3 .