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High Energy Physics - Theory, hep-th, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,Nonlinear Sciences, Exactly Solvable and Integrable Systems, nlin.SI
Abstract:
In the past years, there have been tremendous advances in the field of planar
N=4 super Yang-Mills scattering amplitudes. At tree-level they were formulated
as Grassmannian integrals and were shown to be invariant under the Yangian of
the superconformal algebra psu(2,2|4). Recently, Yangian invariant deformations
of these integrals were introduced as a step towards regulated loop-amplitudes.
However, in most cases it is still unclear how to evaluate these deformed
integrals. In this work, we propose that changing variables to oscillator
representations of psu(2,2|4) turns the deformed Grassmannian integrals into
certain matrix models. We exemplify our proposal by formulating Yangian
invariants with oscillator representations of the non-compact algebra u(p,q) as
Grassmannian integrals. These generalize the Brezin-Gross-Witten and
Leutwyler-Smilga matrix models. This approach might make elaborate matrix model
technology available for the evaluation of Grassmannian integrals. Our
invariants also include a matrix model formulation of the u(p,q) R-matrix,
which generates non-compact integrable spin chains.
