Related papers: Permutations and the Loop
We present a complete basis of multi-trace multi-matrix operators that has a diagonal two point function for the free matrix field theory at finite N. This generalises to multiple matrices the single matrix diagonalisation by Schur…
Four-point functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory are studied using N=2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar…
We examine the double-trace spectrum of $\mathcal{N} = 4$ super Yang-Mills theory in the supergravity limit. At large $N$ double-trace operators exhibit degeneracy. By considering free-field and tree-level supergravity contributions to…
The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known…
We report on a systematic perturbative study of three-point functions in planar SU(N) N=4 super Yang-Mills theory at the one-loop level involving scalar field operators up to length five. For this we have computed a sample of 40 structure…
Noncommutative ${\cal N}=1$ and ${\cal N}=2$ supersymmetric Yang-Mills theories with gauge group U(N) are studied here using the background field method and superspace background covariant D-algebra in perturbation theory. At one loop…
We develop a compact representation of the one-loop n-point functions of all chiral primary operators in planar SU(N), N=4 super Yang-Mills theory in terms of tree-level disk correlation functions and the scalar one-loop box integral. As a…
The superconformal group of N=4 super-Yang-Mills has two types of operator representations: short and long. We conjecture that operator product expansions for which at least two of the three operators are short exactly respect a bonus…
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 compute the one-loop four-point function in {\cal N}=4 supersymmetric Yang-Mills theory with gauge group U(N). We perform the calculation in {\cal N}=1 superspace using the background field method and obtain the complete off-shell…
We propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous 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…
We determine the one-loop deformation of the conformal symmetry of a general N}=2 superconformally invariant Yang-Mills theory. The deformation is computed for several explicit examples which have a realization as world-volume theories on a…
We generalize the unifying relations for tree amplitudes to the $1$-loop Feynman integrands. By employing the $1$-loop CHY formula, we construct differential operators which transmute the $1$-loop gravitational Feynman integrand to Feynman…
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…
Basso, Komatsu and Vieira recently proposed an all-loop framework for the computation of three-point functions of single-trace operators of ${\cal N}=4$ super-Yang-Mills, the "hexagon program". This proposal results in several remarkable…
We derive an infinite sequence of Schwinger-Dyson equations for $N=1$ supersymmetric Yang-Mills theory. The fundamental and the only variable employed is the Wilson-loop geometrically represented in $N=1$ superspace: it organizes an…
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop…
We study the $n$-point functions of scalar multi-trace operators in the $U(N_c)$ gauge theory with adjacent scalars, such as ${\cal N}=4$ super Yang-Mills, at tree-level by using finite group methods. We derive a set of formulae of the…
We re-consider operator mixing in the so-called $SU(2)$ sector of ${\cal N} \, = \, 4$ super Yang-Mills theory with gauge group $SU(N)$. Where possible, single-trace operators of moderate length are completed by higher-trace admixtures so…