On Instantons in Holographic QCD

We examine instantons and solitons of the effective action of probe D8-branes in the background of $N_c$ D4-branes which has served as a holographic description of QCD. We show that the 4d instantons sit at the minimum of the Euclidean 5d action. Restricting to the static solitons of the five-dimensional model we are led to consider monopoles in a 3-dimensional curved space. Since the background metric depends only on the fifth coordinate, it is possible to reduce the monopole equations to the ones in flat space and write down the explicit solutions.