Graßmannian integrals in Minkowski signature, amplitudes, and integrability

Abstract

We attempt to systematically derive tree-level scattering amplitudes in four-dimensional, planar, maximally supersymmetric Yang-Mills theory from integrability. We first review the connections between integrable spin chains, Yangian invariance, and the construction of such invariants in terms of Graßmannian contour integrals. Building upon these results, we equip a class of Graßmannian integrals for general symmetry algebras with unitary integration contours. These contours emerge naturally by paying special attention to the proper reality conditions of the algebras. Specializing to psu(2, 2|4) and thus to maximal superconformal symmetry in Minkowski space, we find in a number of examples expressions similar to, but subtly different from the perturbative physical scattering amplitudes. Our results suggest a subtle breaking of Yangian invariance for the latter, with curious implications for their construction from integrability.

Constructing $$ \mathcal{N} $$ = 4 Coulomb branch superamplitudes

“…The breaking of dual conformality at loop level by IR divergences is understood from the Wilson loop duality [50] and has been used to fully determine the amplitudes with fewer than six legs [51]. However, the extent of the usefulness and survival of the enhancements in scattering amplitudes at loop-level is still under investigation [52][53][54][55][56], although some of the progress has made use of this at the level of the loop integrands where infrared divergences can be sidestepped.…”