ABJM amplitudes and WL at finite N

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.

On the ABJM four-point amplitude at three loops and BDS exponentiation

“…The available two-loop results for amplitudes in ABJM exhibit uniform transcendentality. This is true even for non-planar corrections [35,36] and seems to be a property of the ABJM S-matrix, at least at four points. Recently this intuition has been given an explanation in terms of a construction of amplitudes using on-shell graphs [37] similar to that for N = 4 SYM [38].…”

On form factors in N = 4 $$ \mathcal{N}=4 $$ SYM theory and polytopes

“…Strong coupling limit results for the form factors were obtained in [32,33]. The form factors in theories with maximal supersymmetry in dimensions different from D = 4 were investigated in [34,35,36].…”

The 1/2 BPS Wilson loop in ABJ(M) at two loops: the details

“…On the one hand scattering amplitudes of N = 6 supersymmetric Chern-Simons-matter theories [14]- [25] have been computed and they have been found to exhibit nice symmetry properties as in four dimensional N = 4 SYM. Their allegedly dual objects, namely light-like polygonal Wilson loops have been also calculated [26]- [28], and the emergence of a duality with amplitudes have been observed at four points.…”