Are scattering amplitudes dual to super Wilson loops?

TL;DR

This paper investigates the proposed duality between scattering amplitudes and Wilson loops in N=4 SYM, revealing that quantum corrections break the symmetry and invalidate the duality for non-MHV amplitudes.

Contribution

It demonstrates that supersymmetric Wilson loops do not preserve the necessary symmetries at the quantum level, challenging the extension of the amplitude/Wilson loop duality beyond MHV amplitudes.

Findings

Quantum corrections break chiral supersymmetry at one loop.

Supersymmetric Wilson loops exhibit a conformal anomaly at one loop.

The proposed duality does not hold for non-MHV amplitudes at quantum level.

Abstract

The MHV scattering amplitudes in planar N=4 SYM are dual to bosonic light-like Wilson loops. We explore various proposals for extending this duality to generic non-MHV amplitudes. The corresponding dual object should have the same symmetries as the scattering amplitudes and be invariant to all loops under the chiral half of the N=4 superconformal symmetry. We analyze the recently introduced supersymmetric extensions of the light-like Wilson loop (formulated in Minkowski space-time) and demonstrate that they have the required symmetry properties at the classical level only, up to terms proportional to field equations of motion. At the quantum level, due to the specific light-cone singularities of the Wilson loop, the equations of motion produce a nontrivial finite contribution which breaks some of the classical symmetries. As a result, the quantum corrections violate the chiral supersymmetry already at one loop, thus invalidating the conjectured duality between Wilson loops and non-MHV scattering amplitudes. We compute the corresponding anomaly to one loop and solve the supersymmetric Ward identity to find the complete expression for the rectangular Wilson loop at leading order in the coupling constant. We also demonstrate that this result is consistent with conformal Ward identities by independently evaluating corresponding one-loop conformal anomaly.