Towards the two-loop Lcc vertex in Landau gauge

Details Towards the two-loop Lcc vertex in Landau gauge Towards the two-loop Lcc vertex in Landau gauge

2006-04-16

arxiv.org/abs/hep-th/0604112v2

Int.J.Mod.Phys.A22:1905-1934,2007

Physics

High Energy Physics

High Energy Physics - Theory

27 pp, 2 figures, Latex2e, revised version, to appear in IJMPA, references added, comments on nonsupersymmetric case added

Scientific paper

10.1142/S0217751X0703618X

We are interested in the structure of the Lcc vertex in the Yang-Mills theory, where c is the ghost field and L the corresponding BRST auxiliary field. This vertex can give us information on other vertices, and the possible conformal structure of the theory should be reflected in the structure of this vertex. There are five two-loop contributions to the Lcc vertex in the Yang-Mills theory. We present here calculation of the first of the five contributions. The calculation has been performed in the position space. One main feature of the result is that it does not depend on any scale, ultraviolet or infrared. The result is expressed in terms of logarithms and Davydychev integral J(1,1,1) that are functions of the ratios of the intervals between points of effective fields in the position space. To perform the calculation we apply Gegenbauer polynomial technique and uniqueness method.

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