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  Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-6383-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0027-12A4-7
Genre: Journal Article

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 Creators:
Kanning, Nils, Author
Ko, Yumi, Author
Staudacher, Matthias1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: 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.

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 Dates: 2014-12-2920152015
 Publication Status: Published in print
 Pages: 15 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1412.8476
DOI: 10.1016/j.nuclphysb.2015.03.011
 Degree: -

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Title: Nuclear Physics B
Source Genre: Journal
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Publ. Info: Amsterdam : North-Holland
Pages: - Volume / Issue: 894 Sequence Number: - Start / End Page: 407 - 421 Identifier: ISSN: 0550-3213
CoNE: /journals/resource/954925564667