A note on two-loop superloop

TL;DR

This paper investigates the duality between supersymmetric Wilson loops and NMHV scattering amplitudes, confirming the preservation of supersymmetry at two loops in a simplified kinematic setting.

Contribution

It provides a two-loop calculation of a super Wilson loop component, demonstrating the cancellation of anomalies and the dual conformal invariance of the remainder function.

Findings

Confirmed supersymmetry preservation at two loops in a restricted kinematic setup.

Derived a dual conformally invariant remainder function consistent with NMHV amplitudes.

Showed systematic anomaly subtraction at one-loop extends to two-loop calculations.

Abstract

We explore the duality between supersymmetric Wilson loop on null polygonal contours in maximally supersymmetric Yang-Mills theory and next-to-maximal helicity violating (NMHV) scattering amplitudes. Earlier analyses demonstrated that the use of a dimensional regulator for ultraviolet divergences, induced due to presence of the cusps on the loop, yields anomalies that break both conformal symmetry and supersymmetry. At one-loop order, these are present only in Grassmann components localized in the vicinity of a single cusp and result in a universal function for any number of sites of the polygon that can be subtracted away in a systematic manner leaving a well-defined supersymmetric remainder dual to corresponding components of the superamplitude. The question remains though whether components which were free from the aforementioned supersymmetric anomaly at leading order of perturbation theory remain so once computed at higher orders. Presently we verify this fact by calculating a particular component of the null polygonal super Wilson loop at two loops restricting the contour kinematics to a two-dimensional subspace. This allows one to perform all computations in a concise analytical form and trace the pattern of cancellations between individual Feynman graphs in a transparent fashion. As a consequence of our consideration we obtain a dual conformally invariant result for the remainder function in agreement with one-loop NMHV amplitudes.