Abstract
In this paper we present a new compact expression of the elliptic genus of SL(2)/U(1)-supercoset theory by making use of the ‘spectral flow method’ of the pathintegral evaluation. This new expression is written in a form like a Poincaré series with a non-holomorphic Gaussian damping factor, and manifestly shows the modular and spectral flow properties of a real analytic Jacobi form. As a related problem, we present similar compact formulas for the modular completions of various mock modular forms which appear in the representation theory of \( \mathcal{N}=2,\;4 \) superconformal algebras.
We further discuss the generalization to the cases of arbitrary spin-structures, that is, the world-sheet fermions with twisted boundary conditions parameterized by a continuous parameter. This parameter is naturally identified with the ‘u-variable’ in the Appell-Lerch sum.
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ArXiv ePrint: 1407.7721
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Eguchi, T., Sugawara, Y. Compact formulas for the completed mock modular forms. J. High Energ. Phys. 2014, 156 (2014). https://doi.org/10.1007/JHEP11(2014)156
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DOI: https://doi.org/10.1007/JHEP11(2014)156