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Based on general considerations such as $R$-operation and Slavnov-Taylor identity we show that the effective action, being understood as Legendre transform of the logarithm of the path integral, possesses particular structure in ${\cal N} =4$ supersymmetric Yang--Mills theory for kernels of the effective action expressed in terms of the dressed effective fields. These dressed effective fields have been introduced in our previous papers as actual variables of the effective action. The concept of dressed effective fields naturally appears in the framework of solution to Slavnov-Taylor identity. The particularity of the structure is the independence of these kernels on the ultraviolet regularization scale $\Lambda.$ These kernels are functions of mutual spacetime distances and of the gauge coupling. The fact that $\beta$ function in this theory is zero is used significantly., Comment: 9 pages, 2 figures, figures added and IR divergency discussed

We consider effective action for the Einstein gravity and show that dressed mean fields are actual variables of the effective action. Kernels of this effective action expressed in terms of dressed effective fields are constituent parts of scattering amplitudes for gravitons. Possible applications to the graviton scattering and black hole formation are discussed at the semiclassical level. In particular, we consider graviton scattering in four dimensions based on the Lipatov effective action for quantum gravity, shock waves of particles moving on the brane in Randall-Sundrum scenario with fifth extra dimension, and Giddings' estimation of Froissart bound., Comment: 11 pages, no figures

We argue in favor of the independence on any scale, ultraviolet or infrared, in kernels of the effective action expressed in terms of dressed N =1 superfields for the case of N =4 super-Yang--Mills theory. Under ``finiteness'' of the effective action of dressed mean superfields we mean its ``scale independence''. We use two types of regularization: regularization by dimensional reduction and regularization by higher derivatives in its supersymmetric form. Based on the Slavnov--Taylor identity we show that dressed fields of matter and of vector multiplets can be introduced to express the effective action in terms of them. Kernels of the effective action expressed in terms of such dressed effective fields do not depend on the ultraviolet scale. In the case of dimensional reduction, by using the developed technique we show how the problem of inconsistency of the dimensional reduction can be solved. Using Piguet and Sibold formalism, we indicate that the dependence on the infrared scale disappears off shell in both the regularizations., Comment: 12 pages, revised version, references added

We consider a particular solution to Slavnov-Taylor identity in four-dimensional supergravity. The consideration is performed for pure supergravity, no matter superfields are included. The solution is obtained by inserting dressing functions into ghost part of the classical action for supergravity.As a consequence, physical part of the effective action is local invariant with respect to diffeomorphism and structure groups of transformation for dressed effective superfields of vielbein and spin connection., 6 pages, minor changes, to appear in Mod.Phys.Lett.A