Instantons on Sasakian 7-manifolds

Abstract We study a natural contact instanton equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related to both the transverse Hermitian Yang–Mills (HYM) condition and G2-instanton equation. obtain, by Fredholm theory, finite-dimensional local model for moduli space of irreducible solutions. Following approach Baraglia Hekmati in five dimensions [1], we derive cohomological conditions smoothness express its dimension terms index elliptic operator. Finally, show that self-dual instantons Kähler, case. As an instance concrete interest, specialize transversely holomorphic bundles Calabi–Yau 7-manifolds, as studied Calvo-Andrade, Rodríguez Sá Earp [8], this context notions instanton, integrable HYM connection coincide.