ADHM Construction of (Anti-)Self-dual Instantons in Eight Dimensions

We study the ADHM construction of (anti-)self-dual instantons in eight dimensions. We propose the general scheme to construct the (anti-)self-dual gauge field configurations $F \wedge F = \pm *_8 F \wedge F$ whose finite topological charges are given by the fourth Chern number. We show that our construction reproduces the known $\text{SO}(8)$ one-instanton solution. We also construct multi-instanton solutions of 't Hooft and Jackiw-Nohl-Rebbi (JNR) types in the dilute instanton gas approximation. The well-separated configurations of multi-instantons reproduce the correct topological charges with high accuracy. We also show that our construction is generalized to (anti-)self-dual instantons in $4n \ (n=3,4, \ldots)$ dimensions.Comment: 35 pages, 1 figure, minor correction

Atiyah-Manton construction of Skyrmions in eight dimensions

We show that the eight-dimensional instanton solution, which satisfies the self-duality equation $F \wedge F = *_8 F \wedge F$, realizes the static Skyrmion configuration in eight dimensions through the Atiyah-Manton construction. The relevant energy functional of the Skyrme field is obtained by the formalism developed by Sutcliffe. By comparing the Skyrmion olution associated with the extreme of the energy, with the Atiyah-Manton solution constructed by the instantons, we find that they agree with high accuracy. This is a higher-dimensional analogue of the Atiyah-Manton construction of Skyrmions in four dimensions. Our result indicates that the instanton/Skyrmion correspondence seems to be an universal property in $4k \ (k=1, 2, \ldots)$ dimensions.Comment: 23 pages, 5 figures, published versio

Effect of atmospheric-controlled induction-heating fine particle peening on wear resistance and fatigue properties of maraging steel fabricated by laser powder-bed fusion

Maraging steel components fabricated by laser powder-bed fusion, which is a technique of additive manufacturing, are expected to be used widely because of their high strength, hardness and toughness. To apply maraging steel manufactured by laser powder-bed fusion in wider industrial fields and prevent the components from fracture, a study was conducted to improve the wear resistance and fatigue properties of the steel by an atmospheric-controlled induction-heating fine particle peening surface modification technique. The technique developed can create hard intermetallic compound layers and introduce peening effects, which are expected to improve the wear resistance and fatigue properties of maraging steel fabricated by laser powder-bed fusion. The prepared specimens were examined using optical microscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy, laser microscopy, X-ray diffraction, micro-Vickers hardness testing, nano-indentation testing, reciprocating ball-on-disk wear tests and axial fatigue tests. It was revealed that atmospheric-controlled induction-heating fine particle peening using mechanically milled particles formed Fe–Al intermetallic compound layers with high hardness, introduced compressive residual stresses and increased the hardness of the maraging steel substrate owing to age hardening. In conclusion, atmospheric-controlled induction-heating fine particle peening can simultaneously improve the wear resistance and fatigue properties of maraging steel fabricated by laser powder-bed fusion within a few minutes. These achievements can expand applications of maraging steel fabricated by laser powder-bed fusion