Abstract
In this paper, we present a candidate for mathcal {N}=(1,1) extended higher-spin AdS_3 supergravity with the most general boundary conditions discussed by Grumiller and Riegler recently. We show that the asymptotic symmetry algebra consists of two copies of the mathfrak {osp}(3|2)_k affine algebra in the presence of the most general boundary conditions. Furthermore, we impose some certain restrictions on gauge fields on the most general boundary conditions and that leads us to the supersymmetric extension of the Brown–Henneaux boundary conditions. We eventually see that the asymptotic symmetry algebra reduces to two copies of the mathcal {SW}(frac{3}{2},2) algebra for mathcal {N}=(1,1) extended higher-spin supergravity.
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