Effective action of dressed mean fields for N = 4 super-Yang-Mills theory

TL;DR

This paper demonstrates that in ${ m N}=4$ super-Yang-Mills theory, the effective action's kernels expressed in terms of dressed effective fields are independent of the UV regularization scale, leveraging the theory's zero beta function.

Contribution

It introduces a specific structure of the effective action in ${ m N}=4$ SYM using dressed fields, highlighting their scale independence and relation to Slavnov-Taylor identities.

Findings

Kernels depend only on spacetime distances and gauge coupling.

Effective action structure is independent of the UV regularization scale.

Zero beta function plays a crucial role in the analysis.

Abstract

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.