On the Effective Action of Dressed Mean Fields for $\mathcal N=4$ Super-Yang–Mills Theory

On the basis of the 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 $\mathcal N=4$ 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 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 vanishes is used significantly.