Graßmannian integral for non-compact oscillator Yangian invariants

Abstract:

Recently there has been much progress in the understanding of
(deformed) tree-level scattering amplitudes of N=4 super Yang-Mills
theory. These amplitudes are invariant under the Yangian of psu(2,2|4)
and they can be formulated in terms of Graßmannian integrals. We show
that, after introducing a crucial new ingredient, this formulation can
also be applied to Yangian invariants for oscillator representations of
the non-compact algebra u(p,q). We discuss sample invariants including,
in particular, the analogue of the u(p,q) R-matrix. Excitingly, our
formulation allows us to identify one class of Yangian invariants with
partition functions of unitary matrix models.