The Konishi multiplet at strong coupling

TL;DR

This work develops a first-principles method to compute the strong-coupling anomalous dimensions of short operators in ${\\cal N}=4$ SYM by quantizing Type IIB strings on $AdS_5\\times S^5$ with the pure spinor formalism. Applying it to the Konishi multiplet, the authors extract the strong-coupling expansion of its conformal dimension from the worldsheet physical-state condition, obtaining $\\Delta=2\\sqrt[4]{\\lambda}+2+{2\\over\\sqrt[4]{\\lambda}}+\\mathcal{O}(\\lambda^{-1/2})$ for the chosen state with $\\Delta_0=6$. The derivation combines a quadratic fluctuation analysis around a point-like string, central-charge corrections to the Virasoro constraint, and controlled quartic contributions, yielding a one-loop strong-coupling correction term of $\\tfrac{2}{\\sqrt[4]{\\lambda}}$. The results agree with Y-system predictions and previous semiclassical/bosonic-string extrapolations, and establish a framework to compute the full massive spectrum at strong coupling within the pure spinor AdS string formalism.

Abstract

We introduce a method to compute from first principles the anomalous dimension of short operators in N=4 super Yang-Mills theory at strong coupling, where they are described in terms of superstring vertex operators in an anti-de Sitter background. We focus on the Konishi multiplet, dual to the first massive level of the superstring, and compute the one-loop correction to its anomalous dimension at strong coupling, using the pure spinor formalism for the superstring.