Systematics of Quarter BPS operators in N=4 SYM

TL;DR

This paper systematically constructs 1/4 BPS operators in N=4 superconformal Yang-Mills theory, distinguishing between protected operators and descendants, and demonstrates their protected dimensions to order g^2.

Contribution

It introduces a systematic method to identify 1/4 BPS operators and proves their protected dimensions at order g^2 using superspace and component techniques.

Findings

1/4 BPS operators have protected dimensions to order g^2.

Operators are classified into those containing 1/4 BPS operators and descendants.

Orthogonality defines quantum 1/4 BPS operators.

Abstract

A systematic construction is presented of 1/4 BPS operators in N=4 superconformal Yang-Mills theory, using either analytic superspace methods or components. In the construction, the operators of the classical theory annihilated by 4 out of 16 supercharges are arranged into two types. The first type consists of those operators that contain 1/4 BPS operators in the full quantum theory. The second type consists of descendants of operators in long unprotected multiplets which develop anomalous dimensions in the quantum theory. The 1/4 BPS operators of the quantum theory are defined to be orthogonal to all the descendant operators with the same classical quantum numbers. It is shown, to order $g^2$, that these 1/4 BPS operators have protected dimensions.