Patrick Desrosiers, Luc Lapointe, Pierre Mathieu
We uncover a deep connection between the N=1 superconformal field theory in 2D and eigenfunctions of the supersymmetric Sutherland model known as Jack superpolynomials (sJacks). Specifically, the singular vector at level rs/2 of the Kac module labeled by the two integers r and s can be obtained explicitly as a sum of sJacks whose indexing diagrams are contained in a rectangle with r columns and s rows. As a second compelling evidence for the distinguished status of the sJack-basis in SCFT, we find that the degenerate Whittaker vectors (Gaiotto states), in both the Neveu-Schwarz and Ramond sectors, can be expressed rather simply in terms of sJacks. As a consequence, we are able to reformulate the supersymmetric version of the (degenerate) AGT conjecture in terms of the combinatorics of sJacks.
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http://arxiv.org/abs/1205.0784
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