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We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N=4 super Yang-Mills theory are invariant under a Yangian symmetry Y[psu(2,2|4)] built upon the manifest superconformal symmetry algebra of the theory.…
I provide a new idea based on geometric analysis to obtain a positive mass gap in pure non-abelian renormalizable Yang-Mills theory. The orbit space, that is the space of connections of Yang-Mills theory modulo gauge transformations, is…
We exploit a conjectured continuity between super Yang-Mills on $\mathbb R^3\times \mathbb S^1$ and pure Yang-Mills to study $k$-strings in the latter theory. As expected, we find that Wilson-loop correlation functions depend on the N-ality…
We express all correlation functions in timelike boundary Liouville theory as unitary matrix integrals and develop efficient techniques to evaluate these integrals. We compute large classes of correlation functions explicitly, including an…
We study the lattice model for the supersymmetric Yang-Mills theory in two dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal proof for the absence of susy breaking counter terms as well as the stability of the…
We study the question whether matrix models obtained in the zero volume limit of 4d Yang-Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi-Kawai model in terms of Hermitian matrices, but…
We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su$(2|3)$ sector of ${\cal N}=4$ super Yang-Mills theory, have a bare dimension $\sim N$ and are a linear…
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice…
We consider SU($N$) Yang-Mills theory on ${\mathbb R}^{2,1}\times S^1$, where $S^1$ is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on ${\mathbb R}^{2,1}$…
Correlation functions of the FF and F\tilde{F} operators in hot SU(3) Yang-Mills theory have recently been studied both on the lattice and in perturbation theory, and the results subsequently compared to the strong coupling limit of…
A gauge invariant infrared regularization of the Yang-Mills theory applicable beyond perturbation theory is constructed.
We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying…
We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory away from the origin of the moduli space and demonstrate that the results are extremely simple, in much the same way as in the conformally invariant theory.…
We report recent results and developments from our ongoing lattice studies of $\mathcal N = 4$ supersymmetric Yang--Mills theory. These include a proof that only a single fine-tuning needs to be performed, so long as the moduli space is not…
Supersymmetric Yang-Mills (SYM) theories in four dimensions exhibit many interesting non-perturbative phenomena that can be studied by means of Monte Carlo lattice simulations. However, the lattice regularization breaks supersymmetry…
We compute $e^{-AN}$ corrections to the Gross-Taylor 1/N expansion of the paritition function of two-dimensional SU(N) and U(N) Yang Mills theory. We find a very similar structure of mixing between holomorphic and anti-holomorphic sectors…
We show that the massive Yang--Mills action having as a mass term the non-local operator introduced by Gubarov, Stodolsky, and Zakharov is classically equivalent to a principal gauged sigma model. The non-local mass corresponds to the…
Based on the AdS/CFT correspondence, string theory has given exact predictions for circular Wilson loops in U(N) ${\cal N}=4$ supersymmetric Yang-Mills theory to all orders in a 1/N expansion. These Wilson loops can also be derived from…
We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of…
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…