Alladi Ramakrishnan Hall

D-instantons and mock modular forms

Sibasish Banerjee

IPhT, CEA, Saclay

I'll discuss the modular properties of D3-brane instantons appearing in Calabi-Yau string compactifications. I'll show that
the D3-instanton contribution to a certain geometric potential on the hypermultiplet moduli space can be related to the elliptic
genus of (0,4) SCFT. The modular properties of the potential imply that the elliptic genus associated with non-primitive divisors
of Calabi-Yau is only mock modular. I'll show how to construct its modular completion and prove the modular invariance of the
twistorial construction of D-instanton corrected hypermultiplet moduli space.