Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence

Abstract

We compute non-extremal three-point functions of scalar operators in $\mathcal{N}=4$ super Yang-Mills at tree-level in $g_{YM}$ and at finite $N_c$, using the operator basis of the restricted Schur characters. We make use of the diagrammatic methods called quiver calculus to simplify the three-point functions. The results involve an invariant product of the generalized Racah-Wigner tensors ($6j$ symbols). Assuming that the invariant product is written by the Littlewood-Richardson coefficients, we show that the non-extremal three-point functions satisfy the large $N_c$ background independence; correspondence between the string excitations on $Ad{S}_5\times S^5$ and those in the LLM geometry.

arXiv comment55 pages, v2, v3: typo corrected. To appear in JHEP

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