Transcendentality of ABJM two-point functions

TL;DR

This paper demonstrates that two-point functions of certain operators in ABJM theory exhibit uniform transcendentality up to two loops, suggesting a deeper mathematical structure that simplifies their calculation.

Contribution

It provides the first explicit two-loop calculation of ABJM two-point functions and conjectures the all-order transcendentality property, aiding future computations.

Findings

Two-loop two-point functions show uniform transcendentality.

Conjecture that transcendentality holds at all orders.

Streamlined reconstruction of master integrals using Euler sums.

Abstract

We compute the two-point function of protected dimension-1 operators in ABJM up to two loops in dimensional regularization. The result exhibits uniform transcendentality empirically, which we conjecture to hold at all orders. We leverage this property to streamline the reconstruction of the dimensional regularization expansion of master integrals in terms of bases of Euler sums of uniform transcendental weight.