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

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Cited by in corpus (26)

• Exact Multi-Matrix Correlators
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• Nonplanar Integrability
• Giant Graviton Oscillators
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• Surprisingly Simple Spectra
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• From counting to construction of BPS states in N=4 SYM
• Schur-Weyl duality as an instrument of Gauge-String duality
• Emergent Threebrane Lattices
• Correlators in Nontrivial Backgrounds
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Non-planar Anomalous Dimensions in the sl(2) Sector
• Cut-and-join operators and N=4 super Yang-Mills
• BPS Chaos
• Quarter BPS classified by Brauer algebra
• Correlators Of Operators with a Large R-charge
• Exciting LLM Geometries
• Integrable Subsectors from Holography
• Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons
• Flavour singlets in gauge theory as Permutations
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• Emergent Yang-Mills theory
• Negative anomalous dimensions in N=4 SYM
• Anomalous dimensions from boson lattice models
• Non-planar operator mixing by Brauer representations