Revisiting instanton corrections to the Konishi multiplet

Abstract

We revisit the calculation of instanton effects in correlation functions in $\mathcal{N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these operators do not receive instanton corrections in the semiclassical approximation. We go beyond this approximation and demonstrate that, while operators belonging to the same $\mathcal{N}=4$ supermultiplet ought to have the same conformal data, the evaluation of quantum instanton corrections for one operator can be mapped into a semiclassical computation for another operator in the same supermultiplet. This observation allows us to compute explicitly the leading instanton correction to the scaling dimension of operators in the Konishi supermultiplet as well as to their structure constants in the OPE of two half-BPS scalar operators. We then use these results, together with crossing symmetry, to determine instanton corrections to scaling dimensions of twist-four operators with large spin.

25 pages; v2: minor changes, typos corrected

References in corpus (2)

• Comments on operators with large spin
• On level crossing in conformal field theories

Cited by in corpus (11)

• More $\mathcal{N}=4$ superconformal bootstrap
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Handling Handles. Part II. Stratification and Data Analysis
• Resurgence of the dressing phase for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Instanton effects in correlation functions on the light-cone
• Instanton corrections to twist-two operators
• On instanton effects in the operator product expansion
• S-duality invariant perturbation theory improved by holography
• Lieb-Schultz-Mattis Theorem and the Filling Constraint
• On interpolating anomalous dimension of twist-two operators with general spins