Principal W-algebras for GL(m|n)

We consider the (finite) $W$-algebra $W_{m\mathrm{\mid }n}$ attached to the principal nilpotent orbit in the general linear Lie superalgebra ${\mathfrak{g}\mathfrak{l}}_{m\mathrm{\mid }n}(\mathbb{C})$. Our main result gives an explicit description of $W_{m\mathrm{\mid }n}$ as a certain truncation of a shifted version of the Yangian $Y({\mathfrak{g}\mathfrak{l}}_{1\mathrm{\mid }1})$. We also show that $W_{m\mathrm{\mid }n}$ admits a triangular decomposition and construct its irreducible representations.