Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 002, 8 pages      math-ph/0601002

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

Gorazd Cvetic a, Igor Kondrashuk a, b and Ivan Schmidt a
a) Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Casilla 110-V, Valparaiso, Chile
b) Departamento de Ciencias Basicas, Universidad del Bio-Bio, Campus Fernando May, Casilla 447, Avenida Andreas Bello, Chillan, Chile

Received October 30, 2005, in final form January 01, 2006; Published online January 09, 2006

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 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 Λ. These kernels are functions of mutual spacetime distances and of the gauge coupling. The fact that β function in this theory vanishes is used significantly.

Key words: R-operation; gauge symmetry; N = 4 supersymmetry; Slavnov-Taylor identity.

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