Abstract
Let X be a Calabi-Yau 4-fold and D a smooth divisor on it. We consider tautological complex associated with L=OX(D) on the moduli space of Le Potier stable pairs and define its counting invariant by integrating the Euler class against the virtual class. We conjecture a formula for their generating series expressed using genus zero Gopakumar-Vafa invariants of D and genus one Gopakumar-Vafa type invariants of X, which we verify in several examples. When X is the local resolved conifold, our conjecture reproduces a conjectural formula of Cao-Kool-Monavari in the PT chamber. In the JS chamber, we completely determine the invariants and use it to confirm one of our previous conjectures.
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