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

Vincent Bouchard , Thomas Creutzig , Duiliu-Emanuel Diaconescu , Charles Doran , Callum Quigley , Artan Sheshmani

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classification ✦ hep-th math.AG

keywords boundd4-d2-d0formulamodularitystatesverticalcalabi-yauconstruction

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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.

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

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