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Journal Article

Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants


Staudacher,  Matthias
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Kanning, N., Ko, Y., & Staudacher, M. (2015). Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants. Nuclear Physics B, 894, 407-421. doi:10.1016/j.nuclphysb.2015.03.011.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-6383-7
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.