Related papers: Integrable Spin Chain and Operator Mixing in N=1,2…

We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building…

We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the…

Recently it was established that the one-loop planar dilatation generator of N=4 Super Yang-Mills theory may be identified, in some restricted cases, with the Hamiltonians of various integrable quantum spin chains. In particular Minahan and…

Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1|2) sector. For planar N=4 SYM…

In this chapter of "Review of AdS/CFT Integrability" we introduce N=4 Super Yang-Mills. We discuss the global superalagebra PSU(2,2|4) and its action on gauge invariant operators. We then discuss the computation of the correlators of…

We argue that existing methods for the perturbative computation of anomalous dimensions and the disentanglement of mixing in N = 4 gauge theory can be considerably simplified, systematized and extended by focusing on the theory's dilatation…

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find…

The complete one-loop, planar dilatation operator of the N=4 superconformal gauge theory was recently derived and shown to be integrable. Here, we present further compelling evidence for a generalisation of this integrable structure to…

The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of SU(4) is not manifest in the N=1 formulation of the theory but rather uses an equation of motion. On the classical level one finds one…

The relation between the dilatation operator of N=4 Yang-Mills theory and integrable spin chains makes it possible to compute the one-loop anomalous dimensions of all operators in the theory. In this paper we show how to apply the…

We investigate the structure of the dilatation operator D of planar N=4 SYM in the sector of single trace operators built out of two chiral combinations of the 6 scalars. Previous results at low orders in `t Hooft coupling \lambda suggest…

We study the anomalous dimensions for scalar operators for a three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We show that the mixing matrix at two-loop order is that for an integrable Hamiltonian of an SU(4) spin…

We study insertions of composite operators into Wilson loops in N=4 supersymmetric Yang-Mills theory in four dimensions. The loops follow a circular or straight path and the composite insertions transform in the adjoint representation of…

We consider N=1, D=4 superconformal U(N)^{pq} Yang-Mills theories dual to AdS_5xS^5/Z_pxZ_q orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector…

The large N limit of the anomalous dimensions of operators in ${\cal N}=4$ super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Young diagrams that have two columns (both long) so…

We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective Hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program…

We analyze the one-loop correction to the three-point function coefficient of scalar primary operators in N=4 SYM theory. By applying constraints from the superconformal symmetry, we demonstrate that the type of Feynman diagrams that…

We study supersymmetric Wilson loop operators in four-dimensional N=4 super Yang-Mills theory. We show that the contour of a supersymmetric Wilson loop is either an orbit of some conformal transformation of the space-time (case I), or an…

We investigate the one-loop spectral problem of $\gamma$-twisted, planar $\mathcal{N}$=4 Super Yang-Mills theory in the double-scaling limit of infinite, imaginary twist angle and vanishing Yang-Mills coupling constant. This non-unitary…

The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while…