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PreprintCC BY 4.0arXiv

Free-field realizations of ๐’ฉ = 1 supersymmetric ๐’ฒ-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$

  • Naozumi Tanabe
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Abstract

We extend the recursive construction of free-field realizations proposed by Ide, Ito, and Miyazaki to the ๐’ฉ = 1 supersymmetric ๐’ฒ-algebras ๐’ฎ๐’ฒ B (n โˆ’ 1 , n) and ๐’ฎ๐’ฒ B (n , n), associated with the Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$, respectively. We obtain explicit free-field realizations of ๐’ฎ๐’ฒ B (0 , 1), ๐’ฎ๐’ฒ B (1 , 1), ๐’ฎ๐’ฒ B (1 , 2), and ๐’ฎ๐’ฒ B (2 , 2). In particular, the realizations of ๐’ฎ๐’ฒ B (1 , 2) and ๐’ฎ๐’ฒ B (2 , 2) are new. Using these realizations, we compute central charges, conformal weights, and eigenvalues of the generating currents on free-field highest-weight states, and construct the local integrals of motion I1, I3, and I5.

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Cite

BibTeXRIS
BibTeX
@misc{tanabe2026freefield,
  title = {{Free-field realizations of $\mathcalN = 1$ supersymmetric $\mathcalW$-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$}},
  author = {Naozumi Tanabe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27853},
  eprint = {2610.27853},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27853},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Free-field realizations of ๐’ฉ = 1 supersymmetric ๐’ฒ-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$
AU  - Naozumi Tanabe
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27853
UR  - https://arxiv.org/abs/2610.27853
AB  - We extend the recursive construction of free-field realizations proposed by Ide, Ito, and Miyazaki to the ๐’ฉ = 1 supersymmetric ๐’ฒ-algebras ๐’ฎ๐’ฒ B (n โˆ’ 1 , n) and ๐’ฎ๐’ฒ B (n , n), associated with the Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$, respectively. We obtain explicit free-field realizations of ๐’ฎ๐’ฒ B (0 , 1), ๐’ฎ๐’ฒ B (1 , 1), ๐’ฎ๐’ฒ B (1 , 2), and ๐’ฎ๐’ฒ B (2 , 2). In particular, the realizations of ๐’ฎ๐’ฒ B (1 , 2) and ๐’ฎ๐’ฒ B (2 , 2) are new. Using these realizations, we compute central charges, conformal weights, and eigenvalues of the generating currents on free-field highest-weight states, and construct the local integrals of motion I_1, I_3, and I_5.
ER  -