Mock modularity from black hole scattering states

Sameer Murthy*, Boris Pioline

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The exact degeneracies of quarter-BPS dyons in Type II string theory on K3 × T2 are given by Fourier coefficients of the inverse of the Igusa cusp form. For a fixed magnetic charge invariant m, the generating function of these degeneracies naturally decomposes as a sum of two parts, which are supposed to account for single-centered black holes, and two-centered black hole bound states, respectively. The decomposition is such that each part is separately modular covariant but neither is holomorphic, calling for a physical interpretation of the non-holomorphy. We resolve this puzzle by computing the supersymmetric index of the quantum mechanics of two-centered half-BPS black-holes, which we model by geodesic motion on Taub-NUT space subject to a certain potential. We compute a suitable index using localization methods, and find that it includes both a temperature-independent contribution from BPS bound states, as well as a temperature-dependent contribution due to a spectral asymmetry in the continuum of scattering states. The continuum contribution agrees precisely with the non-holomorphic completion term required for the modularity of the generating function of two-centered black hole bound states.

Original languageEnglish
Article number119
JournalJournal of High Energy Physics
Issue number12
Publication statusPublished - 1 Dec 2018


  • Black Holes in String Theory
  • Solitons Monopoles and Instantons
  • Supersymmetry and Duality


Dive into the research topics of 'Mock modularity from black hole scattering states'. Together they form a unique fingerprint.

Cite this