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

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 $\mathcal{N}=4$ 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 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.

arXiv comment9 pages, 2 figures, figures added and IR divergency discussed

References in corpus (8)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Higher covariant derivative regularization revisited
• Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD
• Universal invariant renormalization of supersymmetric Yang-Mills theory
• QCD effective action with dressing functions - consistency checks in the perturbative regime
• An approach to solve Slavnov-Taylor identities in nonsupersymmetric non-Abelian gauge theories

Cited by in corpus (13)

• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Glauber - Gribov approach for DIS on nuclei in N=4 SYM
• Towards the two-loop Lcc vertex in Landau gauge
• Solution to Bethe-Salpeter equation via Mellin-Barnes transform
• New four-dimensional integrals by Mellin-Barnes transform
• Fourier transforms of UD integrals
• Transformations of triangle ladder diagrams
• Further results for the two-loop Lcc vertex in the Landau gauge
• Gluon self-interaction in the position space in Landau gauge
• Finiteness of N =4 super-Yang-Mills effective action in terms of dressed N =1 superfields
• Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions
• Semiclassical scattering amplitudes of dressed gravitons
• Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals