Anomalous Dimensions from a Spinning D5-Brane
Adi Armoni
TL;DR
This work extends the holographic computation of twist-two operator anomalous dimensions to antisymmetric representations in N=4 SYM by modeling the bound state of k coincident strings as a spinning D5-brane wrapping an S4 in S5. The main result, E−J = Δ−J = (2N√λ/3π^2) sin^3 θ_k log J with θ_k tied to k/N, is derived from a D5-brane action with worldvolume flux and independently cross-checked via cusped Wilson loops, yielding γ_antisymmetric/γ_fundamental = (2N/3π) sin^3 θ_k. The paper discusses the validity, limits, and potential transitions between perturbative Casimir scaling and the strong-coupling D5-brane description, and hints at connections to spin-chain dynamics. These results deepen the understanding of how higher-rank representations map to brane configurations in AdS/CFT and how Wilson loop techniques illuminate operator dimensions at strong coupling.
Abstract
We consider the anomalous dimension of a certain twist two operator in N=4 super Yang-Mills theory. At strong coupling and large-N it is captured by the classical dynamics of a spinning D5-brane. The present calculation generalizes the result of Gubser, Klebanov and Polyakov (hep-th/0204051): in order to calculate the anomalous dimension of a bound state of k coincident strings, the spinning closed string is replaced by a spinning D5 brane that wraps an S4 inside the S5 part of the AdS5 times S5 metric.