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We give the large N limit of the effective potential for the O(N) linear sigma model in four dimensions in terms of the Lambert W function. The effective potential is fully consistent with the renormalization group, and it admits an…
We study the large N anomalous dimensions of operators in a Leigh-Strassler deformation of N=4 super Yang-Mills theory. The operators that we study have a bare dimension of order N (so that the large N limit is not captured by planar…
Consequences of a strong version of the AdS/CFT correspondence for extremely stringy physics are examined. In particular, properties of N = 4 supersymmetric Yang-Mills theory are used to extract results about interacting tensionless strings…
A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six…
A semiclassical string description is given for correlators of Wilson loops with local operators in N=4 SYM theory in the regime when operators carry parametrically large R-charge. The OPE coefficients of the circular Wilson loop in chiral…
In a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the classical non-conservation equations. We apply this…
The operator product expansion for ``small'' Wilson loops in {\cal N}=4, d=4 SYM is studied. The OPE coefficients are calculated in the large N and g_{YM}^2 N limit by exploiting the AdS/CFT correspondence. We also consider Wilson surfaces…
The result for the six-loop anomalous dimension of twist-three operators in the planar N=4 SYM theory is presented. The calculations were performed along the paper arXiv:0912.1624. This result provides a new data for testing the proposed…
Yang--Mills theories in four space-time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang--Mills…
We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with and 4 on graphs. By means of extensive simulations, we show that the global pattern of scaling behaviours is analogous to the one…
A non-perturbative Renormalization Group approach is used to calculate scaling functions for an O(4) model in d=3 dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of…
The anomalous dimensions of single-trace local Wilson operators with covariant derivatives in maximally supersymmetric gauge theory are believed to be generated from a deformed noncompact sl(2) Baxter equation. We perform a systematic…
Following our earlier work we argue in detail for the equivalence of the nonlinear $\sigma$ model with Hopf term at~$\theta=\pi/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $\sigma$ model and show the…
We present the result of a full direct component calculation for the first three even moments of the non-planar contribution into the four-loop anomalous dimension of twist-2 operators in maximally extended N=4 supersymmetric Yang-Mills…
We study the $\frac{1}{2}$-BPS circular Wilson loop in the totally antisymmetric representation of the gauge group in $\mathcal N =4 $ supersymmetric Yang-Mills. This observable is captured by a Gaussian matrix model with appropriate…
The $N=4$ supersymmetric self-dual Yang-Mills theory in a four- dimensional space with signature $(2,2)$ is formulated in harmonic superspace. The on-shell constraints of the theory are reformulated in the equivalent form of vanishing…
As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $\mathcal N=2$ 4d superconformal models we consider two special theories with gauge groups $SU(N)$ and…
We study correlation functions on the Coulomb branch of planar $\mathcal{N} = 4$ super-Yang- Mills theory (SYM), and their relationship with integrability, the operator product expansion (OPE), the sum rule, the large charge expansion, and…
The off-shell dynamics of the O(3) nonlinear sigma-model is probed in terms of spectral densities and two-point functions by means of the form factor approach. The exact form factors of the Spin field, Noether-current, EM-tensor and the…
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…