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arXiv · 1504.01849

Elliptic Genera and Characteristic $q$-Series of Superconformal Field Theory

L. Bonora·A. A. Bytsenko·M. Chaichian
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Abstract

We analyze the characteristic series, the $KO$ series and the series associated with the Witten genus, and their analytic forms as the $q$-analogs of classical special functions (in particular $q$-analog of the beta integral and the gamma function). $q$-series admit an analytic interpretation in terms of the spectral Ruelle functions, and their relations to appropriate elliptic modular forms can be described. We show that there is a deep correspondence between the characteristic series of the Witten genus and $KO$ characteristic series, on one side, and the denominator identities and characters of $N=2$ superconformal algebras, and the affine Lie (super)algebras on the other. We represent the characteristic series in the form of double series using the Hecke-Rogers modular identity.

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L. Bonora, A. A. Bytsenko, M. Chaichian. 2015-04-08. Elliptic Genera and Characteristic $q$-Series of Superconformal Field Theory. https://doi.org/10.1016/j.nuclphysb.2015.03.030

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