Related papers: The Dilatation Operator of Conformal N=4 Super Yan…
The dilatation generator measures the scaling dimensions of local operators in a conformal field theory. In this thesis we consider the example of maximally supersymmetric gauge theory in four dimensions and develop and extend techniques to…
We perform an explicit two-loop calculation of the dilatation operator acting on single trace Wilson operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in N=2 and N=4 supersymmetric Yang-Mills…
We continue the analysis of hep-th/0303060 in the one-loop sector and present the complete psu(2,2|4) dilatation operator of N=4 Super Yang-Mills theory. This operator generates the matrix of one-loop anomalous dimensions for all local…
The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal SU(2,2|N) symmetry should possess universal integrability properties for different N. We provide further support for this…
We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find…
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…
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…
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 compute the three-loop anomalous dimension of the BMN operators with charges J=0 (the Konishi multiplet) and J=1 in N=4 super-Yang-Mills theory. We employ a method which effectively reduces the calculation to two loops. Instead of using…
The spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang-Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its $sl(2)$ subsector spanned…
We study the two-loop dilatation operator in the noncompact SL(2) sector of QCD and supersymmetric Yang-Mills theories with N=1,2,4 supercharges. The analysis is performed for Wilson operators built from three quark/gaugino fields of the…
Anomalous dimensions of high-twist Wilson operators in generic gauge theories occupy a band of width growing logarithmically with their conformal spin. We perform a systematic study of its fine structure in the autonomous SL(2) subsector of…
The dilatation operator of planar N=4 super Yang-Mills in the pure scalar SO(6) sector is derived at the two-loop order. Representation theory allows for eight free coefficients in an ansatz for the corresponding spin-chain hamiltonian…
The task of calculating operator dimensions in the planar limit of N=4 super Yang-Mills theory can be vastly simplified by mapping the dilatation generator to the Hamiltonian of an integrable spin chain. The Bethe ansatz has been used in…
We consider the nonplanar universal anomalous dimension of twist-two operators at four loops in N=4 supersymmetric Yang-Mills theory and push its direct diagrammatic calculation through Lorentz spin j=20, one unit beyond the state of the…
We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in…
The dilatation operator measures scaling dimensions of local operator in a conformal field theory. Algebraic methods of constructing the dilatation operator in four-dimensional N=4 gauge theory are reviewed. These led to the discovery of…
We perform direct diagrammatic calculations of the anomalous dimensions of twist-two operators in extended N=2 and N=4 super Yang-Mills theories (SYM). In the case of N=4 SYM, we compute the four-loop anomalous dimension of the twist-two…
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…
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…