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TMF, 2016, Volume 189, Number 3, Pages 380–388 (Mi tmf9252)  

This article is cited in 4 scientific papers (total in 4 papers)

Cyclic gradings of Lie algebras and Lax pairs for $\sigma$-models

D. V. Bykov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We study a class of $\sigma$-models with complex homogeneous target spaces and zero-curvature representations. We find a relation between these models and $\sigma$-models with certain $m$-symmetric target spaces. We also describe a model with the hypercomplex target space $S^1\times S^3$ in detail.

Keywords: $\sigma$-model, integrable system, complex structure

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/tmf9252

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English version:
Theoretical and Mathematical Physics, 2016, 189:3, 1734–1741

Bibliographic databases:

Document Type: Article
Received: 11.07.2016

Citation: D. V. Bykov, “Cyclic gradings of Lie algebras and Lax pairs for $\sigma$-models”, TMF, 189:3 (2016), 380–388; Theoret. and Math. Phys., 189:3 (2016), 1734–1741

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  • http://mi.mathnet.ru/eng/tmf/v189/i3/p380

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. Bykov, “Complex structure-induced deformations of $\sigma$-models”, J. High Energy Phys., 2017, no. 3, 130, front matter+26 pp.  crossref  mathscinet  zmath  isi  scopus
    2. V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. D. Bykov, “Sigma models with complex, graded and eta-deformed target spaces”, Phys. Part. Nuclei, 49:5 (2018), 963–965  crossref  isi  scopus
    4. Bykov D., “Flag Manifold SIGMA-Models: the 1/N-Expansion and the Anomaly Two-Form”, Nucl. Phys. B, 941 (2019), 316–360  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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