On the uniqueness of the octonionic instanton solution on conformally flat 8-manifolds

23rd International Conference on Integrable Systems and Quantum Symmetries

Bilge, A.H.^1

Kadir Has University, Turkey^1

关键词: Instantons;    Orthonormal frames;    Self-dual;    Self-duality;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012011/pdf
DOI  :  10.1088/1742-6596/670/1/012011

来源: IOP

【 摘 要 】

LetMbe an 8-manifold and E be an SO(8) bundle on M. In a previous paper [F. Ozdemir and A.H. Bilge, "Self-duality in dimensions 2n > 4: equivalence of various definitions and the derivation of the octonionic instanton solution", ARI (1999) 51:247-253], we have shown that if the second Pontrjagin number p2of the bundle E is minimal, then the components of the curvature 2-form matrix F with respect to a local orthonormal frame are Fij= cijωij, where cij's are certain functions and the ωij's are strong self-dual 2-forms such that for all distinct i, j, k, l, the products ωijωjkare self dual and ωijωklare anti self-dual. We prove that if the cij's are equal to each other and the manifold M is conformally flat, then the octonionic instanton solution given in [B.Grossman, T.W.Kephart, J.D.Stasheff, Commun. Math. Phys., 96, 431-437, (1984)] is unique in this class.