ABJM amplitudes and WL at finite N

TL;DR

This paper computes two-loop ABJM amplitudes and Wilson loop observables for any gauge group rank N, revealing insights into non-planar contributions, IR divergences, and the non-abelian exponentiation theorem, supporting the uniform transcendentality principle.

Contribution

It provides the first explicit two-loop non-planar ABJM amplitude and Wilson loop results at finite N, extending previous planar analyses and confirming the transcendentality principle.

Findings

IR divergences at subleading order are proportional to leading poles

Derived a general expression for the two-loop Sudakov form factor at any N

Results support the validity of the uniform transcendentality principle beyond the planar limit

Abstract

We evaluate ABJM observables at two loops, for any value of the rank N of the gauge group. We compute the color subleading contributions to the four-point scattering amplitude in ABJM at two loops. Contrary to the four dimensional case, IR divergent N-subleading contributions are proportional to leading poles in the regularization parameter. We then exploit the non-planar calculation for the amplitude to derive an expression for the two-loop Sudakov form factor at any N. In the planar limit the result coincides with the one recently obtained in literature by using Feynman diagrams and unitarity. Finally, we analyze the subleading contributions to the light-like four-cusps Wilson loop and interpret the result in terms of the non-abelian exponentiation theorem. All these perturbative results satisfy the uniform transcendentality principle, hinting at its validity in ABJM beyond the planar limit.