Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM_4

TL;DR

This work analyzes perturbative and instanton corrections to the OPE of lowest weight Chiral Primary Operators in N=4 SYM4 to test dynamical predictions from AdS/CFT. It demonstrates a perturbative splitting of free-field operators, including the stress tensor and R-symmetry current, into multiple supermultiplets with distinct anomalous dimensions, and clarifies which double-trace operators remain non-renormalized or acquire finite dims at strong coupling. The authors perform a 2-loop analysis of the OPE via the four-point function and extract explicit anomalous-dimension patterns across SU(4) irreps, revealing a Konishi-like structure for several operators while others stay protected. Instanton contributions are shown to affect only those double-trace operators with finite strong-coupling dimensions, with a universal ratio connecting strong-coupling and instanton effects, while Konishi and certain multiplets remain uninfluenced by instantons.

Abstract

We study perturbative and instanton corrections to the Operator Product Expansion of the lowest weight Chiral Primary Operators of N=4 SYM_4. We confirm the recently observed non-renormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that appear to be unprotected by unitarity restrictions. We demonstrate the splitting of the free-field theory stress tensor and R-symmetry current in supermultiplets acquiring different anomalous dimensions in perturbation theory and argue that certain double-trace operators also undergo a perturbative splitting into operators dual to string and two-particle gravity states respectively. The instanton contributions affect only those double-trace operators that acquire finite anomalous dimensions at strong coupling. For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.