On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains

Kang Lu (Department of Mathematics, University of Virginia, 141 Cabell Dr, Charlottesville, VA, 22903, USA)

We study the gl m n $$ {\mathfrak{gl}}_{m\mid n} $$ XXX spin chains defined on tensor products of highest weight gl m n $$ {\mathfrak{gl}}_{m\mid n} $$ -modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues. Then we take the classical limits and obtain the corresponding results for the gl m n $$ {\mathfrak{gl}}_{m\mid n} $$ Gaudin models.

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      "source": "Springer", 
      "value": "We study the   <math> <msub> <mi>gl</mi> <mrow> <mi>m</mi> <mo>\u2223</mo> <mi>n</mi> </mrow> </msub> </math>  $$ {\\mathfrak{gl}}_{m\\mid n} $$  XXX spin chains defined on tensor products of highest weight   <math> <msub> <mi>gl</mi> <mrow> <mi>m</mi> <mo>\u2223</mo> <mi>n</mi> </mrow> </msub> </math>  $$ {\\mathfrak{gl}}_{m\\mid n} $$ -modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues. Then we take the classical limits and obtain the corresponding results for the   <math> <msub> <mi>gl</mi> <mrow> <mi>m</mi> <mo>\u2223</mo> <mi>n</mi> </mrow> </msub> </math>  $$ {\\mathfrak{gl}}_{m\\mid n} $$  Gaudin models."
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Published on:
24 April 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 4
Pages 1-40
DOI:
https://doi.org/10.1007/JHEP04(2023)120
arXiv:
2209.14416
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: