Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories

TL;DR

We address the AdS/CFT correspondence for the infinite family of $AdS_5\times Y^{p,q}$ backgrounds by mapping long BPS operators in the dual toric quivers to massless geodesics on $Y^{p,q}$ and by extending the analysis to BMN-type fluctuations.A reduced, first-order action for strings with large $Q_R$ is derived, together with a spin-chain description of holomorphic long operators, yielding an effective worldsheet dynamics that mirrors the bulk geometry and the BPS geodesic structure.The mesonic chiral ring is organized into basic blocks $\mathcal{S}$, $\mathcal{L}_+$, $\mathcal{L}_-$, with the full ring given by $\mathcal{O}_{s,l}=\mathcal{S}^s\mathcal{L}^l$, and the BPS/geodesic dictionary is fixed by charges via relations such as $P_\alpha=-3y_0Q_R$ and $J=\tfrac{1}{2}(1-y_0)Q_R$, with $y_0\in[y_1,y_2]$.Beyond BPS, the paper discusses a special conformal-point where the chiral ring is enhanced, analyzes near-BPS excitations, and demonstrates that a spin-chain effective action can reproduce, in the large-$Q_R$ limit, features of the semiclassical string action, providing evidence for the emergence of a string picture from the gauge theory.

Abstract

We study the AdS/CFT relation between an infinite class of 5-d Ypq Sasaki-Einstein metrics and the corresponding quiver theories. The long BPS operators of the field theories are matched to massless geodesics in the geometries, providing a test of AdS/CFT for these cases. Certain small fluctuations (in the BMN sense) can also be successfully compared. We then go further and find, using an appropriate limit, a reduced action, first order in time derivatives, which describes strings with large R-charge. In the field theory we consider holomorphic operators with large winding numbers around the quiver and find, interestingly, that, after certain simplifying assumptions, they can be described effectively as strings moving in a particular metric. Although not equal, the metric is similar to the one in the bulk. We find it encouraging that a string picture emerges directly from the field theory and discuss possible ways to improve the agreement.