Multiple D3-instantons and mock modular forms I

Understand

We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold.

• In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus.
• We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role.
• We focus on the contact potential, an analogue of the Kahler potential which must transform as a modular form under S-duality.