Permutations and the Loop

Abstract

We consider the one-loop two-point function for multi-trace operators in the U(2) sector of \cN=4 supersymmetric Yang-Mills at finite N. We derive an expression for it in terms of U(N) and S_{n+1} group theory data, where n is the length of the operators. The Clebsch-Gordan operators constructed in 0711.0176, which are diagonal at tree level, only mix at one loop if you can reach the same (n+1)-box Young diagram by adding a single box to each of the n-box Young diagrams of their U(N) representations (which organise their multi-trace structure). Similar results are expected for higher loops and for other sectors of the global symmetry group.

13+7 pages, 9 figures; references added, minor clarification

References in corpus (6)

• Single-top hadroproduction in association with a W boson
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Supergravitons from one loop perturbative N=4 SYM
• Half-BPS SU(N) Correlators in N=4 SYM

Cited by in corpus (3)

• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• Schur-Weyl duality as an instrument of Gauge-String duality
• Correlators Of Operators with a Large R-charge