On Operator Mixing in N=4 SYM

TL;DR

This paper analyzes the mixing of scalar operators in N=4 SYM, calculating their anomalous dimensions at order g^2, and discusses implications for holographic duality and operator decoupling.

Contribution

It provides the first detailed calculation of operator mixing and anomalous dimensions for specific scalar operators in N=4 SYM, including the absence of instantonic effects.

Findings

Order g^2 corrections to anomalous dimensions computed

Ratios of results are irrational numbers

Double-trace operators decouple in the large N limit

Abstract

We resolve the mixing of the scalar operators of naive dimension 4 belonging to the representation 20' of the SU(4) R-symmetry in N=4 SYM. We compute the order g^2 corrections to their anomalous dimensions and show the absence of instantonic contributions thereof. Ratios of the resulting expressions are irrational numbers, even in the large N limit where, however, we observe the expected decoupling of double-trace operators from single-trace ones. We briefly comment on the generalizations of our results required in order to make contact with the double scaling limit of the theory conjectured to be holographically dual to type IIB superstring on a pp-wave.