Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N

Abstract

We study all three-point functions of normalized chiral operators in D=4, $\mathcal{N}=4$, U(N) supersymmetric Yang-Mills theory in the large $N$ limit. We compute them for small 't Hooft coupling $\lambda=g_{YM}^2N<<1$ using free field theory and at strong coupling $\lambda=g_{YM}^2>>1$ using the $AdS$/CFT correspondence. Surprisingly, we find the same answers in the two limits. We conjecture that at least for large $N$ the exact answers are independent of $\lambda $ .