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We review the basic results concerning the structure of effective action in N=4 supersymmetric Yang-Mills theory in Coulomb phase. Various classical formulations of this theory are considered. We show that the low-energy effective action depending on all fileds of N=4 vector multiplet can be exactly found. This result is discussed on the base of algebraic analysis exploring the general harmonic superspace techniques and on the base of straightforward quantum field theory calculations using the N=2 supersymmetric background field method. We study the one-loop effective action beyond leading low-energy approximation and construct supersymmetric generalization of Heisenberg-Euler-Schwinger effective action depending on all fields of N=4 vector multiplet. We also consider the derivation of leading low-enrgy effective action at two loops.
We present $mathcal{N}=2$ superconformal $mathsf{U}(1)$ duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the lo
We compute the one-loop non-holomorphic effective potential for the N=4 SU(n) supersymmetric Yang-Mills theory with the gauge symmetry broken down to the maximal torus. Our approach remains powerful for arbitrary gauge groups and is based on the use
We construct a manifestly N=3 supersymmetric low-energy effective action of N=3 super Yang-Mills theory. The effective action is written in the N=3 harmonic superspace and respects the full N=3 superconformal symmetry. On mass shell this action is re
We present the technique for resummation of flux tube excitations series arising in pentagon operator expansion program for polygonal Wilson loops in N=4 SYM. Here we restrict ourselves with contributions of one-particle effective states and consider
In this paper we study the form factors for the half-BPS operators $mathcal{O}^{(n)}_I$ and the $mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $mathcal{K}$ at fi