Instantons on Cylindrical Manifolds

Abstract

We consider an instanton,$\text{A}$,with $L^2$-curvature $F_{\text{A}}$ on the cylindrical manifold $Z=\mathbf{R}\times M$,where $M$ is a closed Riemannian $n$-manifold, $n\ge 4$.We assume $M$ admits a $3$-form $P$ and a $4$-form $Q$ satisfy $dP=4Q$ and $d\ast Q=(n-3)\ast P$.Manifolds with these forms include nearly Kähler 6-manifolds and nearly parallel $G_2$-manifolds in dimension 7.Then we can prove that the instanton must be a flat connection.

All comments are welcome. Add the esitimation of curvature of Yang-Mills connection with torsion

References in corpus (3)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Gauge Theory in higher dimensions, II
• Generalised Chern-Simons Theory and ${\mathrm{G}}_2$-Instantons over Associative Fibrations