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Uspekhi Mat. Nauk, 2017, Volume 72, Issue 1(433), Pages 37–106 (Mi umn9754)  

This article is cited in 7 scientific papers (total in 7 papers)

Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors

A. A. Hutsalyuka, A. Liashykbcd, S. Z. Pakulyakaef, E. Ragoucyg, N. A. Slavnovh

a Moscow Institute of Physics and Technology
b Bogoliubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine
c National Research University "Higher School of Economics"
d Skolkovo Institute of Science and Technology
e Joint Institute for Nuclear Research
f A. I. Alikhanov Institute for Theoretical and Experimental Physics
g Laboratoire d'Annecy-le-Vieux de Physique Théorique (LAPTH), Annecy-le-Vieux, France
h Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians $Y(\mathfrak{gl}(m|n)$ in terms of the current generators of the Yangian double $DY(\mathfrak{gl}(m|n))$. The method of projections onto intersections of different types of Borel subalgebras of this infinite-dimensional algebra is used to construct the Bethe vectors. Calculation of these projections makes it possible to express the supersymmetric Bethe vectors in terms of the matrix elements of the universal monodromy matrix. Two different presentations for the Bethe vectors are obtained by using two different but isomorphic current realizations of the Yangian double $DY(\mathfrak{gl}(m|n))$. These Bethe vectors are also shown to obey certain recursion relations which prove their equivalence.
Bibliography: 30 titles.

Keywords: Bethe vector, current algebra, monodromy matrix, Gauss decomposition, projection.

Funding Agency Grant Number
Centre National de la Recherche Scientifique F14-2016
Ministry of Education and Science of the Russian Federation 5-100
Russian Foundation for Basic Research 14-01-00547-а
15-31-20484-мол_а_вед.
N.A.S. thanks LAPTH in Annecy-le-Vieux for their hospitality and stimulating scientific atmosphere and CNRS for partial financial support. The work of A.L. was funded by the Russian Academic Excellence Project (project 5-100) and the joint NASU-CNRS project F14-2016. The work of S.P. was supported in part by the Russian Foundation for Basic Research (grant no. 14-01-00547-a). N.A.S. was supported by the Russian Foundation for Basic Research (grant no. 15-31-20484-мол_а_вед).


DOI: https://doi.org/10.4213/rm9754

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English version:
Russian Mathematical Surveys, 2017, 72:1, 33–99

Bibliographic databases:

ArXiv: 1611.09620
Document Type: Article
UDC: 512.579
MSC: Primary 82B23; Secondary 81R50, 17B80, 17B37
Received: 29.11.2016

Citation: A. A. Hutsalyuk, A. Liashyk, S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors”, Uspekhi Mat. Nauk, 72:1(433) (2017), 37–106; Russian Math. Surveys, 72:1 (2017), 33–99

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry”, Nucl. Phys. B, 923 (2017), 277–311  crossref  zmath  isi  scopus
    2. J. Fuksa, N. A. Slavnov, “Form factors of local operators in supersymmetric quantum integrable models”, J. Stat. Mech. Theory Exp., 2017, 043106, 21 pp.  crossref  mathscinet  isi  scopus
    3. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry”, Nuclear Phys. B, 926 (2018), 256–278  crossref  mathscinet  zmath  isi  scopus
    4. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_n)$”, SciPost Phys., 4:1 (2018), 006  crossref  isi
    5. A. Liashyk, N. A. Slavnov, “On Bethe vectors in $\mathfrak{gl}_3$ -invariant integrable models”, J. High Energy Phys., 2018, no. 6, 018, 31 pp.  crossref  mathscinet  isi  scopus
    6. N. Gromov, F. Levkovich-Maslyuk, “New compact construction of eigenstates for supersymmetric spin chains”, J. High Energy Phys., 2018, no. 9, 085, 22 pp.  crossref  mathscinet  isi  scopus
    7. Liashyk A. Pakuliak S.Z. Ragoucy E. Slavnov N.A., “New Symmetries of Gl(N)-Invariant Bethe Vectors”, J. Stat. Mech.-Theory Exp., 2019, 044001  crossref  isi
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