The topology of moduli spaces of Higgs bundles is related to enumerative invariants of Calami-Yau threefolds using a string theoretic framework. This construction provides a physical derivation for the conjectures of Hausel, Letellier and Rodriguez-Villegas, as well as Hausel, Mereb and Wong on the cohomology of character varieties. Joint work with Wu-yen Chuag, Ron Donagi, Guang Pan and Tony Panted.