Zoom virtual seminar: Click here to enter room
The generating functions of degeneracies of D4-D2-D0 black holes in Type II string compactifications on Calabi-Yau threefolds are example of (higher depth) mock modular forms. I'll explain how S-duality can be used to derive an explicit form for their modular completions, which becomes particularly simple in the presence of a refinement. This result turns out to have many applications going beyond the original context. In particular, I'll show that it can be used
i) to reproduce in a very easy way the known results on modular properties of the generating functions of BPS dyons in N=4 string compactifications;
ii) to find Vafa-Witten invariants of arbitrary(!) rank on CP^2, Hirzebruch and del Pezzo surfaces;
iii) to obtain holomorphic anomaly equations for BPS partition functions;
iv) to reveal a non-commutative structure induced by the refinement on the moduli space of compactified theory.
Zoom link: https://cern.zoom.us/j/94903183761?pwd=SUE5aTIzcnBwVlQ3TjFXdWZSUGdaQT09