Conformal anomaly of super Wilson loop

TL;DR

This paper investigates the conformal anomaly in the super Wilson loop within maximally supersymmetric Yang-Mills theory, demonstrating how to identify and undo the symmetry breaking caused by dimensional regularization at one loop.

Contribution

It provides a detailed analysis of the conformal anomaly in super Wilson loops and introduces a method to restore superconformal symmetry by subtracting the anomaly, enhancing the duality with non-MHV amplitudes.

Findings

Computed the one-loop conformal anomaly for the super Wilson loop.

Showed the anomaly depends on Grassmann coordinates.

Restored superconformal invariance by subtracting the anomaly.

Abstract

Classically supersymmetric Wilson loop on a null polygonal contour possesses all symmetries required to match it onto non-MHV amplitudes in maximally supersymmetric Yang-Mills theory. However, to define it quantum mechanically, one is forced to regularize it since perturbative loop diagrams are not well-defined due to presence of ultraviolet divergences stemming from integration in the vicinity of the cusps. A regularization that is adopted by practitioners by allowing one to use spinor helicity formalism, on the one hand, and systematically go to higher orders of perturbation theory is based on a version of dimensional regularization, known as Four-Dimensional Helicity scheme. Recently it was demonstrated that its use for the super Wilson loop at one loop breaks both conformal symmetry and Poincare supersymmetry. Presently, we exhibit the origin for these effects and demonstrate how one can undo this breaking. The phenomenon is alike the one emerging in renormalization group mixing of conformal operators in conformal theories when one uses dimensional regularization. The rotation matrix to the diagonal basis is found by means of computing the anomaly in the Ward identity for the conformal boost. Presently, we apply this ideology to the super Wilson loop. We compute the one-loop conformal anomaly for the super Wilson loop and find that the anomaly depends on its Grassmann coordinates. By subtracting this anomalous contribution from the super Wilson loop we restore its interpretation as a dual description for reduced non-MHV amplitudes which are expressed in terms of superconformal invariants.