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We uncover a deep connection between the $\mathcal{N}=1$ superconformal fieldtheory in 2D and eigenfunctions of the supersymmetric Sutherland model known asJack superpolynomials (sJacks). Specifically, the singular vector at level$rs/2$ of the Kac module labeled by the two integers $r$ and $s$ are givenexplicitly as a sum of sJacks whose indexing diagrams are contained in arectangle with $r$ columns and $s$ rows As a second compelling evidence for thedistinguished status of the sJack-basis in SCFT, we find that the degenerateWhittaker vectors (Gaiotto states) can be expressed as a remarkably simplelinear combination of sJacks. As a consequence, we are able to reformulate thesupersymmetric version of the (degenerate) AGT conjecture in terms of thecombinatorics of sJacks. Note that the closed-form formulas for the singularvectors and the degenerate Whittaker vectors, although only conjectured ingeneral, have been heavily tested (in some cases, up to level 33/2). Note alsothat both the Neveu-Schwarz and Ramond sectors are treated.

Superconformal field theory and Jack superpolynomials