Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-38

Nils Kanning, Yumi Ko, Matthias Staudacher


Graßmannian Integrals as matrix for Non-Compact Yangian Invariants.


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.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-38