Higher poles and crossing phenomena from twisted genera

Sujay Ashok (1) , Eleonora Dell 'Aquila (1) , Jan Troost (2)

1 IMSc - Institute of Mathematical Sciences [Chennai]
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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 el-liptic 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. A consequence of our analysis is 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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Sujay Ashok, Eleonora Dell 'Aquila, Jan Troost. Higher poles and crossing phenomena from twisted genera. Journal of High Energy Physics, 2014, 2014 (8), pp.29. ⟨10.1007/JHEP08(2014)087⟩. ⟨hal-01074890⟩