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.

22 pages

References in corpus (7)

• Mock Theta Functions
• A Twisted Non-compact Elliptic Genus
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
• $R^3$ index for four-dimensional $N=2$ field theories
• Wall-crossing made smooth
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