Vertical D4-D2-D0 bound states on K3 fibrations and modularity

Understand

An explicit formula is derived for the generating function of vertical D4-D2-D0 bound states on smooth K3 fibered Calabi-Yau threefolds, generalizing previous results of Gholampour and Sheshmani.

• It is also shown that this formula satisfies strong modularity properties, as predicted by string theory.
• This leads to a new construction of vector valued modular forms which exhibits some of the features of a generalized Hecke transform.