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We present the full transseries of the strong-coupling expansion of the cusp anomalous dimension in ${\cal N}=4$ super Yang--Mills theory. This quantity admits an exact representation as a ratio of two determinants with particularly simple…

At finite temperature the free energy density of ${\cal N}=4$ supersymmetric Yang-Mills can be calculated using resummed perturbation theory through the order $\lambda^{5/2}$. Effective field theory methods provide a useful alternative…

We formulate N=4 supersymmetric Yang-Mills theory in terms of soft-collinear effective theory. The effective Lagrangian in soft-collinear effective theory is developed according to the power counting by a small parameter \eta \sim…

We solve Schr\"odinger's equation for the ground-state of {\it four}-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading order approximation are reduced to a…

We consider non-planar contributions to the correlation functions of BMN operators in free N = 4 super Yang Mills theory. We recalculate these non-planar contributions from a different kind of diagram and find some exact agreements. The…

Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an…

We study the structure constants of two conformal primary operators and one spinning operator in planar $\mathcal{N} = 4$ Super-Yang-Mills theory using the hexagon formalism. By analytically continuing in the spin, we derive a formula for…

We use the $K$ special conformal generator in the Fuzzy sphere setup of the Ising CFT to determine primary states. For $\Delta \lesssim 8$, we recover the known primaries and find several new ones, including in the parity-odd sector. We…

Exploiting insights on strings moving in pp-wave backgrounds, we show how open strings emerge from N = 4 SU(M) Yang-Mills theory as fluctuations around certain states carrying R-charge of order M. These states are dual to spherical…

We compute the coefficients of an infinite family of chiral primary operators in the local operator expansion of a circular Wilson loop in N=4 supersymmetric Yang-Mills theory. The computation sums all planar rainbow Feynman graphs. We…

Extending recent work of Kachru and Silverstein, we consider ``orbifolds'' of 4-dimensional $\mathcal{N}=4$ SU(n) super-Yang-Mills theories with respect to discrete subgroups of the SU(4) $R$-symmetry which act nontrivially on the gauge…

Using supersymmetric localization, we consider four-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained from $\mathbb{Z}_n$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory in the large $N$ limit at weak coupling.…

We introduce a simple method to extract the representation content of the spectrum of a system with SU(2) symmetry from its partition function. The method is easily generalized to systems with SO(2,4) symmetry, such as conformal field…

We derive forms of light-state dominance for correlators in CFT$_d$, making precise the sense in which correlators can be approximated by the contribution of light operator exchanges. Our main result is that the four-point function of…

We demonstate the existence of a large $N$ phase transition with respect to the 't Hooft coupling in q-deformed Yang-Mills theory on $S^2$. The strong coupling phase is characterized by the formation of a clump of eigenvalues in the…

Kaluza-Klein compactifications of higher dimensional Yang-Mills theories contain a number of four dimensional scalars corresponding to the internal components of the gauge field. While at tree-level the scalar zero modes are massless, it is…

In this paper we study a phase structure of $5D$ ${\cal N}=1$ super Yang-Mills theory with massive matter multiplets and $SU(N)$ gauge group. In particular, we are interested in two cases: theory with $N_f$ massive hypermultiplets in the…

Planar maximally supersymmetric Yang-Mills theory (N=4 SYM) is a special quantum field theory. A few of its remarkable features are conformal symmetry at the quantum level, evidence of integrability and, moreover, it is a prime example of…

We consider two four-dimensional gauge theories with gauge group $SU(N)$: the $\mathcal{N}=4$ Super Yang-Mills (SYM) theory and the $\mathcal{N}=2$ quiver gauge theory obtained as a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ SYM. In this…

We compute the high-temperature limit of the free energy for four-dimensional N=4 supersymmetric SU(N_c) Yang-Mills theory. At weak coupling we do so for a general ultrastatic background spacetime, and in the presence of slowly-varying…