Uniformly transcendental bases for protected two-point functions

TL;DR

This paper constructs explicit bases of uniformly transcendental master integrals for two-point functions in supersymmetric theories, simplifying calculations and potentially aiding further research.

Contribution

It introduces explicit uniformly transcendental bases for two-point functions in $ ext{N}=4$ SYM and ABJM theories up to four loops, enhancing computational efficiency.

Findings

Bases simplify two-point function calculations

Explicit bases constructed up to four loops in 4D and three loops in 3D

Potential applications in other perturbative computations

Abstract

The perturbative expansion of two-point functions of lowest dimension supersymmetric operators in $\mathcal{N}=4$ SYM and ABJM theory exhibits uniform transcendental weight. Inspired by this, we construct an explicit basis of uniformly transcendental master integrals for these correlators, through four loops in four and three loops in three dimensions. In terms of these bases, the two-point functions simplify to rational linear combinations. Conversely, such explicit bases of uniformly transcendental integrals can be useful for other applications.