REPRESENTATIONS OF AFFINE SUPERALGEBRAS AND MOCK THETA FUNCTIONS
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31_2014_Article_9263.pdf
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Author(s)
Wakimoto, Minoru
Kac, Victor
Date Issued
April 2014
Journal
Transformation Groups
Publisher
Springer US
Citation
Kac, Victor G., and Minoru Wakimoto. “REPRESENTATIONS OF AFFINE SUPERALGEBRAS AND MOCK THETA FUNCTIONS.” Transformation Groups 19.2 (2014): 383–455.
Version
Author's final manuscript
Abstract
We show that the normalized supercharacters of principal admissible modules over the affine Lie superalgebra sℓˆ[subscript 2|1] (resp. psℓˆ[subscript 2|2]) can be modified, using Zwegers’ real analytic corrections, to form a modular (resp. S-) invariant family of functions. Applying the quantum Hamiltonian reduction, this leads to a new family of positive energy modules over the N = 2 (resp.N = 4) superconformal algebras with central charge 3(1 − (2 m + 2)/M), where m ∈ ℤ[subscript ≥0], M ∈ ℤ[subscript ≥2], gcd(2 m + 2, M) = 1 if m > 0 (resp. 6 (m/M − 1), where m ∈ ℤ[subscript ≥1], M ∈ ℤ[subscript ≥2], gcd(2 m, M) = 1 if m > 1), whose modified characters and supercharacters form a modular invariant family.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00031-014-9263-z
