An elliptic triptych

Abstract : We clarify three aspects of non-compact elliptic genera. Firstly, we give a path integral derivation of the elliptic genus of the cigar conformal field theory from its non-linear sigma-model description. The result is a manifestly modular sum over a lattice. Secondly, we discuss supersymmetric quantum mechanics with a continuous spectrum. We regulate the theory and analyze the dependence on the temperature of the trace weighted by the fermion number. The dependence is dictated by the regulator. From a detailed analysis of the dependence on the infrared boundary conditions, we argue that in non-compact elliptic genera right-moving supersymmetry combined with modular covariance is anomalous. Thirdly, we further clarify the relation between the flat space elliptic genus and the infinite level limit of the cigar elliptic genus.
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Journal of High Energy Physics, Springer, 2017, 2017 (10), pp.78. 〈https://link.springer.com〉. 〈10.1007/JHEP10(2017)078〉
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Jan Troost. An elliptic triptych. Journal of High Energy Physics, Springer, 2017, 2017 (10), pp.78. 〈https://link.springer.com〉. 〈10.1007/JHEP10(2017)078〉. 〈hal-01625342〉

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