A note on composite operators in N=4 SYM

TL;DR

This paper examines the structure of composite operators in N=4 super Yang-Mills theory, highlighting how their superfield representations vary across free, interacting, and quantum regimes, and identifying a class of protected operators.

Contribution

It introduces a classification of composite operators based on their superfield realizations and identifies a subset that remains protected from renormalization in the quantum theory.

Findings

Certain operators can be expressed as analytic tensor superfields in the quantum theory.

All series B and C operators are included in the protected class.

Some series A operators saturating unitarity bounds are also protected.

Abstract

We discuss composite operators in N=4 super Yang-Mills theory and their realisations as superfields on different superspaces. The superfields that realise various operators on analytic superspace may be different in the free, interacting and quantum theories. In particular, in the quantum theory, there is a restricted class of operators that can be written as analytic tensor superfields. This class includes all series B and C operators in the theory as well as some series A operators which saturate the unitarity bounds. Operators of this type are expected to be protected from renormalisation.