Geodesic
$\mathcal S$-modular transformation of the $\mathcal N=2$ superconformal algebra characters
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 260-284 Cet article a éte moissonné depuis la source Math-Net.Ru

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The $\mathcal N=2$ superconformal algebra characters have to exhibit modular invariance in order to be appropriately applied in quantum superstring theories. The nonunitary characters are given by higher-level Appell functions and different kinds of Jacobi theta functions are involved within their algebraic structures. Evaluating their $\mathcal T$-modular invariance appears to be quite simple, but verifying their $\mathcal S$-modular invariance entails a serious mathematical physics exploration. In this regard, we use a new vocabulary for Jacobi theta functions, namely “spectral theta functions,” which allows us to come up with the $\mathcal S$-modular transformation of nonunitary (nontrivial) $\mathcal N=2$ characters for the central charge $c=3(1-2p/u)$, where $(u,p)$ is a pair of coprime positive integers.
Keywords: $\mathcal N=2$ superconformal algebra characters, $\mathcal S$-modular transformation, spectral theta functions, higher-level Appell functions. 
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M. R. Bahraminasab; M. Ghominejad. $\mathcal S$-modular transformation of the $\mathcal N=2$ superconformal algebra characters. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 260-284. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a1/

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