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The holographic dual to supergravity instantons in $\rm AdS_5\times S^5/\mathbb{Z}_k$

We investigate the holographic dual to supergravity instanton solutions in $\rm AdS_5\times S^5/\mathbb{Z}_k$, which are described entirely in terms of geodesics on the AdS moduli space. These instantons are expected to be holographically dual to instantons in an $\mathcal{N}=2$ necklace quiver gauge theory in four dimensions with $k$ gauge nodes, at large N. For the supersymmetric instantons we find a precise match between the on-shell actions and the vevs of $\text{Tr}[F^2]$ and $\text{Tr}[F\wedge F]$ computed on both sides of the duality. This correspondence requires an exact identification between the massless supergravity scalars and the dual gauge couplings which we give in detail. We also find a candidate for the supergravity dual of a quasi-instanton in the quiver theory, which is a non-supersymmetric extremal solution.