Affine Super Yangians and Rectangular $W$-superalgebras

In this paper, we construct a homomorphism from the affine super Yangian $Y_{{\text{ve}}_1,{\text{ve}}_2}(\widehat{\mathfrak{s}\mathfrak{l}}(m\mathrm{\mid }n))$ to the universal enveloping algebra of the rectangular $W$-superalgebra $W^k(\mathfrak{g}\mathfrak{l}(ml\mathrm{\mid }nl),(l^{(m\mathrm{\mid }n)}))$. We also show that the image of this homomorphism is dense provided that $k+(m-n)(l-1)\mathrm{\ne }0$.