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We study algebras and correlation functions of local operators at half-BPSinterfaces engineered by the stacks of D5 or NS5 branes in the 4d$\mathcal{N}=4$ super Yang-Mills. The operator algebra in this sector isisomorphic to a truncation of the Yangian $\mathcal{Y}(\mathfrak{gl}_n)$. Thecorrelators, encoded in a trace on the Yangian, are controlled by theinhomogeneous $\mathfrak{sl}_n$ spin chain, where $n$ is the number offivebranes: they are given in terms of matrix elements of transfer matricesassociated to Verma modules, or equivalently of products of Baxter'sQ-operators. This can be viewed as a novel connection between the$\mathcal{N}=4$ super Yang-Mills and integrable spin chains. We also remark onanalogous constructions involving half-BPS Wilson lines.

Correlators on the wall and $\mathfrak{sl}_n$ spin chain