On AdS/CFT duality in the twisted sector of string theory on $Ad{S}_5\times S^5/{\mathbb{Z}}_2$ orbifold background

Abstract

We consider type IIB string theory on an $Ad{S}_5\times S^5/{\mathbb{Z}}_2$ 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 $\zeta (3){\alpha }^{\prime 3}$ term in the type IIB string effective action. We find a solution of type IIB supergravity which represents a resolution of the $Ad{S}_5\times S^5/{\mathbb{Z}}_2$ orbifold singularity 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.

29 pages, 3 figures; v2: an issue of residual irregularity of the $S^1$-fibration over $S^2$ in the resolution of the original orbifold singularity is pointed out, main conclusions are unchanged