Yang-Mills Duals for Semiclassical Strings

TL;DR

This paper explores the duality between semiclassical strings in AdS/CFT and super Yang-Mills theory, deriving anomalous dimensions and verifying string solutions using integrability and matrix models.

Contribution

It provides a detailed analysis of the anomalous dimensions of dual operators and verifies string solutions through integrability and matrix model techniques.

Findings

Derived a simple rational function for the one-loop anomalous dimension in terms of J/L.

Solved integral equations from matrix models to match string theory results.

Identified a critical point at J'=4J, interpreted as an artifact of the Bethe ansatz.

Abstract

We consider a semiclassical multiwrapped circular string pulsating on S_5, whose center of mass has angular momentum J on an S_3 subspace. Using the AdS/CFT correspondence we argue that the one-loop anomalous dimension of the dual operator is a simple rational function of J/L, where J is the R-charge and L is the bare dimension of the operator. We then reproduce this result directly from a super Yang-Mills computation, where we make use of the integrability of the one-loop system to set up an integral equation that we solve. We then verify the results of Frolov and Tseytlin for circular rotating strings with R-charge assignment (J',J',J). In this case we solve for an integral equation found in the O(-1) matrix model when J'< J and the O(+1) matrix model if J'> J. The latter region starts at J'=L/2 and continues down, but an apparent critical point is reached at J'=4J. We argue that the critical point is just an artifact of the Bethe ansatz and that the conserved charges of the underlying integrable model are analytic for all J' and that the results from the O(-1) model continue onto the results of the O(+1) model.