Graßmannian integrals in Minkowski signature, amplitudes, and integrability

Abstract

Abstract We attempt to systematically derive tree-level scattering amplitudes in fourdimensional, 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 p s u 2 , 2 | 4 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right) $$ 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.

Keywords

• Lattice Integrable Models
• Matrix Models
• Scattering Amplitudes
• Supersymmetric Gauge Theory