Dual conformal symmetry at loop level; massive regularization

Abstract: Dual conformal symmetry has had a huge impact on our understanding of planar scattering amplitudes in N=4 super Yang-Mills. At tree level, it combines with the original conformal symmetry generators to a Yangian algebra, a hallmark of integrability, and helps in determining the tree-level amplitudes. The latter are now known in closed form. At loop level, it determines the functional form of the four- and five-point scattering amplitudes to all orders in the coupling constant, and gives restrictions at six points and beyond. The symmetry is best understood at loop level in terms of a novel AdS-inspired infrared regularization which makes the symmetry exact, despite the infrared divergences. This has important consequences for the basis of loop integrals in this theory. Recently, a number of selective reviews have appeared which discuss dual conformal symmetry, mostly at tree level. Here, we give an up-to-date account of dual conformal symmetry, focussing on its status at loop level.