Three-point functions in N = 4 SYM at finite Nc and background independence

A bstract We compute non-extremal three-point functions of scalar operators in 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 (6 j 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 AdS 5 × S 5 and those in the LLM geometry.