Related papers: Integral constraints for $\mathcal{N}=4$ super-Yan…

We construct super-Yang-Mills theories on S4 x R, S4 x S1 and S4 x interval with the field content of maximal SYM, coupled to boundary degrees in the last case. These theories provide building blocks of the `5d uplifts' of gauge theories on…

Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this…

Tremendous ongoing theory efforts are dedicated to developing new methods for QCD calculations. Qualitative rather than incremental advances are needed to fully exploit data still to be collected at the LHC. The maximally supersymmetric…

In this letter, an alternative string theory in twistor space is proposed for describing perturbative N=4 super-Yang-Mills theory. Like the recent proposal of Witten, this string theory uses twistor worldsheet variables and has manifest…

According to the AdS/CFT correspondence, the ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory is studied through its gravity dual whose configuration has two boundaries at the opposite sides of the fifth coordinate. At these boundaries,…

We propose a bootstrap program for the {\it form factor squared} with operator ${\rm tr}(\phi^2)$ in maximally supersymmetric Yang-Mills theory in the planar limit, which plays a central role for perturbative calculations of important…

We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of…

We construct the states and symmetries of N = 4 super-Yang-Mills by tensoring two N = 1 chiral multiplets and introducing two extra SUSY generators. This allows us to write the maximal N = 8 supergravity as four copies of the chiral…

We extend the localization calculation of the 3D Chern-Simons partition function over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined on a…

Using the shadow dependent decoupled Slavnov-Taylor identities associated to gauge invariance and supersymmetry, we discuss the renormalization of the N=4 super-Yang-Mills theory and of its coupling to gauge-invariant operators. We specify…

We consider limits of $\mathcal{N} = 4$ super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are…

Recently it has been shown how a topologically twisted version of ${\cal N}=4$ super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero lattice spacing. The remaining fifteen supersymmetries are…

Three-point functions of analytic (chiral primary) operators in N=4 Yang-Mills theory in four dimensions are calculated using the harmonic superspace formulation of this theory. In the case of the energy-momentum tensor multiplet anomaly…

We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite…

We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a two-sphere S^2. We show that expectation values of certain 1/8 BPS supersymmetric…

Different string theories in twistor space have recently been proposed for describing ${\cal N}=4$ super-Yang-Mills. In this paper, my Strings 2003 talk is reviewed in which a string theory in $(x,\theta)$ space was constructed for…

We compute the complete non-planar integrand for the correlation function of four lightest scalar operators in N=4 super Yang-Mills theory at five-loop order. This is equivalent to the super-correlator of nine stress-tensor multiplets in…

This is a pedagogical review on the integrability-based approach to the three-point function in N=4 supersymmetric Yang-Mills theory. We first discuss the computation of the structure constant at weak coupling and show that the result can…

D=4, N=4 super-Yang-Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D=10 theory. That superspace, in particular the choice of pure spinor variables, is less…

As part of the Snowmass community planning exercise, we highlight an ongoing program of research into the structure of scattering amplitudes in N=4 super-Yang-Mills theory, particularly in the planar limit of a large number of colors. This…