Fractional Multi-Trace Fields of N=4 SYM_4 from AdS/CFT

TL;DR

This paper proves that multi-trace operators in N=4 SYM_4 with specific R-symmetry representations have protected conformal dimensions, using perturbative four-point function evaluations up to order 1/N^2.

Contribution

It introduces an inductive proof that all k-trace operators with certain Young tableau partitions have protected dimensions, extending understanding of operator protection in AdS/CFT.

Findings

All k-trace operators with specified Young tableau are quasi primary with protected dimensions.

Perturbative evaluations confirm protection up to order 1/N^2.

The proof applies to operators constructed from chiral primaries in the SO(6)_R irrep.

Abstract

We prove inductively that every k-trace operator of SO(6)_R irrep with Young tableau partition {r_1,r_2,r_3}, constructed out of k chiral primaries in the twenty dimensional SO(6)_R irrep, leads to a quasi primary field with protected conformal dimension. Our argument is based on perturbative evaluations of certain four point functions up to order 1/N^2.