  We consider type IIB string theory on an $AdS_5 \times S^5/\mathbb{Z}_2$
orbifold background, which should be dual to 4d $\mathcal{N}=2$ superconformal
$SU(N)\times SU(N)$ gauge theory with two bi-fundamental hypermultiplets. The
correlator of two chiral BPS operators from the twisted sector of this quiver
CFT exhibits non-trivial dependence on the 't Hooft coupling $\lambda$ already
in the planar limit. This dependence was recently determined using localisation
and the expansion at large $\lambda$ contains a subleading contribution
proportional to $\zeta(3) \lambda^{-3/2}$. We address the question of how to
reproduce this correction on the string theory side by starting with the
$\zeta(3) \alpha'^3$ term in the type IIB string effective action. We find a
regular solution of type IIB supergravity which represents a resolution of the
$AdS_5 \times S^5/\mathbb{Z}_2$ orbifold and demonstrate that the relevant
light twisted sector states may be identified as additional supergravity 2-form
modes ``wrapping" a finite 2-cycle in the resolution space. Reproducing the
structure of the gauge theory result becomes more transparent in the large
R-charge or BMN-like limit in which the resolved background takes a pp-wave
form with the transverse space being a product of $\mathbb R^4$ and the
Eguchi-Hanson space.

High Energy Physics - Theory