Instantons from geodesics in AdS moduli spaces

Understand

We investigate supergravity instantons in Euclidean $\rm AdS_5\times S^5/\mathbb{Z}_k$.

• These solutions are expected to be dual to instantons of $\mathcal{N}=2$ quiver gauge theories.
• On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges.
• The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: For degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY.