Yang-Mills Duals for Semiclassical Strings

TL;DR

The paper tests the AdS/CFT correspondence by analyzing semiclassical string states in AdS5×S5 and their one-loop SYM duals. It casts the one-loop anomalous dimension problem into integrable SO(6) spin-chain Bethe equations and reduces the thermodynamic limit to O(n) matrix-model–type integral equations, enabling analytic results across multiple R-charge sectors. For pulsating and circular string configurations, it derives simple expressions for the anomalous dimension, γ = (λ m^2 / 4L) α(2−α) and γ = λ J'/L^2 respectively, matching semiclassical string predictions. The work also identifies an apparent Bethe-ansatz artifact at J' = 4J and argues for analytic continuation that yields a consistent set of conserved charges across regimes, reinforcing the deep link between semiclassical strings and integrable gauge-theory structures.

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.