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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 study correlators of four protected (half-BPS) operators in strongly coupled supersymmetric Yang-Mills theory. These are dual to tree-level supergravity amplitudes on AdS${}_5\times$S${}_5$ for various spherical harmonics on the…
The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the…
We propose a new example of the AdS/CFT correspondence between the system of multiple giant gravitons in AdS${}_5 \times {}$S${}^5$ and the operators with $O(N_c)$ dimensions in ${\cal N}=4$ super Yang-Mills. We first extend the mixing of…
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…
We study $\frac{1}{4}$-BPS Wilson loops in four-dimensional SU$(N$) ${\mathcal{N}}=2$ super-Yang-Mills theories with conformal matter in an arbitrary representation $\mathcal{R}$. These operators are formed of two meridians on the…
We propose a nonperturbative framework to study general correlation functions of single-trace operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at large $N$. The basic strategy is to decompose them into fundamental building…
We find generating functions for half BPS correlators in $\mathcal{N}=4$ SYM theories with gauge groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$ by computing the norms of a class of BPS coherent states. These coherent states are built from…
In four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(N)$, we present a closed-form solution for a family of integrated four-point functions involving stress tensor multiplet composites of arbitrary R-charge.…
We study the structure of the four-point correlation function of the lowest-dimension 1/2 BPS operators (stress-tensor multiplets) in the (2,0) six-dimensional theory. We first discuss the superconformal Ward identities and the…
We describe the use of generalized unitarity for the construction of correlation functions of local gauge-invariant operators in general quantum field theories and illustrate this method with several calculations in N=4 super-Yang-Mills…
We consider a double OPE limit of the planar four-point function of stress tensor multiplets in N = 4 SYM theory. Loop integrands for this correlator have been constructed to very high order, but the corresponding integrals are explicitly…
In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory…
In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a…
We carry out a bootstrap study of four-point correlators in 4d $\mathcal{N}=2$ SCFTs which are dual to super Yang-Mills on $AdS_5\times S^3$. We focus on the simplest $\frac{1}{2}$-BPS operators which correspond to the super gluons in the…
We present the full form of a four-point correlation function of large BPS operators in planar N = 4 Super Yang-Mills to any loop order. We do this by following a bootstrap philosophy based on three simple axioms pertaining to (i) the space…
We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N=4 super-Yang-Mills theory. We provide exact, finite-coupling…
Four-point correlation functions are observables of significant interest in holographic field theories. We compute an infinite family of four-point correlation functions of operators in short multiplets of 4D N=4 super Yang-Mills theory in…
The superconformal index of $\mathcal N=4$ super-Yang Mills theory with $U(N)$ gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms…
We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an…