Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-05-26
Nucl.Phys. B536 (1998) 617-656
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX2e: amsart, 34pp. An overall sign error corrected in (4.33) and several consequent formulas, and the presentation streaml
Scientific paper
10.1016/S0550-3213(98)00615-4
We evaluate characters of irreducible representations of the N=2 supersymmetric extension of the Virasoro algebra. We do so by deriving the BGG-resolution of the admissible N=2 representations and also a new 3,5,7...-resolution in terms of twisted massive Verma modules. We analyse how the characters behave under the automorphisms of the algebra, whose most significant part is the spectral flow transformations. The possibility to express the characters in terms of theta functions is determined by their behaviour under the spectral flow. We also derive the identity expressing every $\hat{sl}(2)$ character as a linear combination of spectral-flow transformed N=2 characters; this identity involves a finite number of N=2 characters in the case of unitary representations. Conversely, we find an integral representation for the admissible N=2 characters as contour integrals of admissible $\hat{sl}(2)$ characters.
Feigin B. L.
Sirota V. A.
Tipunin Yu. I.
~Semikhatov ~M. A.
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