The variant of ADHMN construction associated with q-analysis

A q-deformation of the ADHMN caloron construction is considered, under which the anti-selfdual (ASD) conditions of the gauge fields are preserved. It is shown that the q-dependent Nahm data with certain constraints are crucial to determine the ASD gauge fields, as in the case of ordinary caloron construction. As an application of the q-deformed ADHMN construction, we give a q-deformed caloron of Harrington-Shepard type. Some limits of the parameters are also considered.Comment: 13 pages, No figure

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