Systematics of Quarter BPS operators in N=4 SYM
E. D'Hoker, P. Heslop, P. Howe, A. V. Ryzhov
TL;DR
The paper develops a systematic construction of $1/4$ BPS operators in ${\cal N}=4$ SYM using $(4,1,1)$ harmonic superspace and component methods. It classifies scalar operators into candidate $1/4$ BPS primaries and long-descendant mixtures in $SU(4)$ representations $[q,p,q]$, defining primaries by orthogonality to descendants and showing their dimensions are protected to order $g^2$. It provides explicit multiplicities, complete operator bases for several reps, and a dictionary to ${\cal N}=1$ language, resolving prior counting mismatches and reinforcing non-renormalization properties relevant to AdS/CFT.
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.