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

Abstract

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.

v2. 56 pages, some formulas corrected, modularity statement improved

References in corpus (4)

• Symmetries and stabilization for sheaves of vanishing cycles
• D3-instantons, Mock Theta Series and Twistors
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• Flops and the S-duality conjecture

Cited by in corpus (7)

• The Asymptotic Weak Gravity Conjecture in M-theory
• Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
• Black holes and higher depth mock modular forms
• Scaling Black Holes and Modularity
• Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua
• Quiver Asymptotics and Amoeba: Instantons on Toric Divisors of Calabi-Yau Threefolds
• Mock modularity at work, or black holes in a forest