In a N = 1 superspace formulation of N = 4 Yang-Mills theory we obtain the anomalous dimensions of chiral operators with large R charge J → ∞ keeping g 2 N/J 2 finite, to all orders of perturbation theory in the planar limit. Our result proves the conjecture that the anomalous dimensions are indeed finite in the above limit. This amounts to an exact check of the proposed duality between a sector of N = 4 Yang-Mills theory with large R charge J and string theory in a pp-wave background.

In this paper we give all the details of the calculation that we presented in our previous paper arXiv:0712.3522, concerning the four-loop anomalous dimension of the Konishi descendant tr(φZφZ − φφZZ) in the SU(2) sector of the N = 4 planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an N = 1 superspace approach and Gegenbauer polynomial x-space techniques.

We compute two-point functions of chiral operators TrΦ 3 in N = 4 SU (N ) supersymmetric Yang-Mills theory to the order g 4 in perturbation theory. We perform explicit calculations using N = 1 superspace techniques and find that perturbative corrections to the correlators vanish for all N . While at order g 2 the cancellations can be ascribed to the nonrenormalization theorem valid for correlators of operators in the same multiplet as the stress tensor, at order g 4 this argument no longer applies and the actual cancellation occurs in a highly nontrivial way. Our result is obtained in complete generality, without the need of additional conjectures or assumptions. It gives further support to the belief that such correlators are not renormalized to all orders in g and to all orders in N .

No abstract

In the β-deformed N = 4 supersymmetric SU (N ) Yang-Mills theory we study the class of operators O J = Tr(Φ J i Φ k ), i = k and compute their exact anomalous dimensions for N, J → ∞. This leads to a prediction for the masses of the corresponding states in the dual string theory sector. We test the exact formula perturbatively up to two loops. The consistency of the perturbative calculation with the exact result indicates that in the planar limit the oneloop condition g 2 = hh for superconformal invariance is indeed sufficient to insure the exact superconformal invariance of the theory. We present a direct proof of this point in perturbation theory. The O J sector of this theory shares many similarities with the BMN sector of the N = 4 theory in the large R-charge limit.