Wednesday, June 19, 2013

1306.4227 (P. Desrosiers et al.)

Super-Whittaker vector at c=3/2    [PDF]

P. Desrosiers, L. Lapointe, P. Mathieu
The degenerate Whittaker vector of the superconformal algebra can be represented in terms of Jack superpolynomials. However, in this representation the norm of the Whittaker vector involves a scalar product with respect to which the Jack superpolynomials are not orthogonal. In this note, we point out that this defect can be cured at c=3/2 by means of a trick specific to the supersymmetric case. At c=3/2, we thus end up with a closed-form expression for the norm of the degenerate super-Whittaker vector. Granting the super-version of the AGT conjecture, this closed-form expression should be equal to the Z_2-symmetric SU(2) pure-gauge instanton partition function -- the corresponding equality taking the form of a rather nontrivial combinatorial identity.
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