# HET Seminar | Atish Dabholkar, Abdus Salam ICTP, Trieste | "Three Avatars of Mock Modularity" | PCTS, Jadwin 407

Fri, Feb 7, 2020, 1:45 pm
Location:
In particular, I will derive  a holomorphic anomaly equation for the indexed partition function of a two-dimensional CFT2 dual to AdS3 that counts the black hole degeneracies,  and for Vafa-Witten partition function for twisted four dimensional N=4 super Yang-Mills theory on CP2 for the gauge group SO(3) that counts instantons.  The holomorphic kernel of this equation is not modular but mock modular’ and one obtains correct modular properties  only after including certain anomalous’ nonholomorphic boundary contributions. This phenomenon can be related to the holomorphic anomaly of  the elliptic genus of a two-dimensional noncompact supersymmetric sigma model, and in a simpler context of quantum mechanics to the Atiyah-Patodi-Singer  eta invariant.