Triangle UD integrals in the position space

TL;DR

This paper explores triangle UD ladder integrals in position space, demonstrating they can be expressed using the same UD functions as in momentum space, aiding all-order loop calculations in supersymmetric Yang-Mills theory.

Contribution

It establishes a method to represent triangle UD ladder integrals in position space using known UD functions, facilitating advanced loop computations in supersymmetric gauge theories.

Findings

Triangle UD ladder integrals in position space are expressible with the same UD functions as in momentum space.

The representation holds for an arbitrary number of rungs in the ladder diagrams.

This work aids in calculating all-order loop corrections in supersymmetric Yang-Mills theory.

Abstract

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.