Hidden supersymmetry as a key to constructing low-energy superfield effective actions

In this review paper, we outline and exemplify the general method of constructing the supefield low-energy quantum effective action of supersymmetric Yang-Mills (SYM) theories with extended supersymmetry in the Coulomb phase, grounded upon the requirement of invariance under the non-manifest (hidden) part of the underlying supersymmetry. In this way we restore the ${\cal N}=4$ supersymmetric effective actions in $4D, {\cal N}=4$ SYM, ${\cal N}=2$ supersymmetric effective actions in $5D, {\cal N}=2$ SYM and ${\cal N}=(1,1)$ supersymmetric effective actions in $6D, {\cal N}=(1,1)$ SYM theories. The manifest off-shell fractions of the full supersymmetry are, respectively, $4D, {\cal N}=2$, $5D, {\cal N}=1$ and $6D, {\cal N}=(1,0)$ supersymmetries. In all cases the effective actions depend on the corresponding covariant superfield SYM strengths and the hypermultiplet superfields. The whole construction essentially exploits a power of the harmonic superspace formalism.
Comment: 0 + 27 pages, Abstract and sec. 2 slightly modified, typos corrected; Contribution to the Volume in Honor of Andrei A. Slavnov on the occasion of his 80th Birthday. arXiv admin note: text overlap with arXiv:1812.07206, arXiv:hep-th/0111062