Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator

TL;DR

This work probes the strong-coupling regime of the Konishi operator in ${\cal N}=4$ SYM via its AdS$_5\times$S$^5$ string dual. By computing 1-loop corrections to energies of several short semiclassical strings and interpolating to finite spins, the authors extract the leading coefficients in the strong-coupling expansion of the Konishi dimension: $\Delta = 2\lambda^{1/4} + b_0 + b_1\lambda^{-1/4} + b_3\lambda^{-3/4} + \cdots$, with $b_0$ related to the canonical dimension $\Delta_0$ and $b_1=1$; they predict a universal pattern across the Konishi multiplet. The analysis emphasizes a decomposition of the 2-d anomalous dimensions, the role of vertex-operator marginality, and the near-flat-space limit, arguing for universality of the first two coefficients and a transcendental structure entering higher-order terms ($b_3$ with $\zeta(3)$). The results are cross-checked across multiple semiclassical configurations and connected to broader discussions on SUSY constraints and integrability approaches.

Abstract

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b_1=1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.