An approach to solve Slavnov-Taylor identity in D4 N=1 supergravity

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.Comment: 6 pages, minor changes, to appear in Mod.Phys.Lett.

Finiteness of N =4 super-Yang-Mills effective action in terms of dressed N =1 superfields

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 adde

On the Effective Action of Dressed Mean Fields for 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 ${\cal N} = 4$ 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 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.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The solution to Slavnov-Taylor identities in D4 N=1 SYM

D4 N=1 SYM with an arbitrary chiral background superfield as the gauge coupling is considered. The solution to Slavnov-Taylor identities has been given. It has been shown that the solution is unique and allows us to restrict the gauge part of the effective action. Under the effective action in this paper we mean the 1PI diagram generator.Comment: 9 pages, Late

Triangle UD integrals in the position space

We investigate triangle UD ladder integrals in the position space. The investigation is necessary to find an all-order in loop solution for an auxiliary Lcc correlator in Wess-Zumino-Landau gauge of the maximally supersymmetric Yang-Mills theory and to present correlators of dressed mean gluons in terms of it in all loops. We show that triangle UD ladder diagrams in the position space can be expressed in terms of the same UD functions Phi^(L) in terms of which they were represented in the momentum space, for an arbitrary number of rungs.Comment: 9 pages, 2 figures, revised version, two references added, comments are included in the text just after Eq.(1) and Eq.(2), the last paragraph is modified, minor corrections, Eq.(6) is corrected, to appear in JHE