1201.6073 (A. V. Belitsky)

Conformal anomaly of super Wilson loop    [PDF]

A. V. Belitsky

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.

View original: http://arxiv.org/abs/1201.6073