Instantons from geodesics in AdS moduli spaces

TL;DR

This paper explores supergravity instantons in Euclidean AdS_5×S^5/Z_k, linking them to geodesics on moduli spaces, and classifies solutions based on supersymmetry preservation and nilpotency of charge matrices.

Contribution

It explicitly describes extremal instanton solutions as lightlike geodesics on the AdS moduli space and computes their on-shell actions in terms of quantized charges.

Findings

Instantons correspond to lightlike geodesics on the moduli space.

Degree 2 geodesics preserve 8 supercharges, degree 3 are non-SUSY.

Explicit expressions for on-shell actions in terms of charges.

Abstract

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. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.