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

TL;DR

This paper explores the AdS/CFT correspondence for Ypq Sasaki-Einstein manifolds, matching field theory operators to string states and deriving an effective string action from the gauge theory side.

Contribution

It introduces a reduced, first-order action for strings with large R-charge in these geometries, linking field theory operators to string dynamics.

Findings

Matching of BPS operators to massless geodesics confirms AdS/CFT correspondence.

Derivation of an effective string action from field theory operators.

Identification of a metric-like structure describing large winding operators.

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.