Abstract
We demonstrate that Appell-Lerch sums with higher order poles as well as their modular covariant completions arise as partition functions in the cigar conformal field theory with worldsheet supersymmetry. The modular covariant derivatives of the elliptic genus of the cigar give rise to operator insertions corresponding to (powers of) right-moving momentum, left-moving fermion number, as well as a term corresponding to an ordinary zero mode partition sum. To show this, we demonstrate how the right-moving supersymmetric quantum mechanics (and in particular the Hamiltonian and spectral density) depend on the imaginary part of the chemical potential for angular momentum. As a consequence of our analysis we find that varying the imaginary part of the chemical potential for angular momentum on the cigar gives rise to a wall-crossing phenomenon in the bound state contribution to the elliptic genus, while the full elliptic genus is a continuous function of the chemical potential.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
