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

TL;DR

This paper investigates perturbative and instanton effects on the operator product expansion of chiral primary operators in N=4 SYM_4, revealing non-renormalization properties and operator splitting phenomena.

Contribution

It provides new insights into non-renormalization, operator splitting, and instanton effects on the OPE in N=4 SYM_4, including the behavior of double-trace operators.

Findings

Confirmed non-renormalization of certain operators.

Demonstrated splitting of stress tensor and R-symmetry current into supermultiplets.

Showed instanton contributions affect only operators with finite strong-coupling anomalous dimensions.

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.