Dmitri V. Bykov, “Flag Manifold Sigma Models and Nilpotent Orbits”, Modern problems of mathematical and theoretical physics, Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov, Trudy Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 89–98; Proc. Steklov Inst. Math., 309 (2020), 78

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 309, Pages 89–98
DOI: https://doi.org/10.4213/tm4081 (Mi tm4081)

This article is cited in 12 scientific papers (total in 12 papers)

Flag Manifold Sigma Models and Nilpotent Orbits

Dmitri V. Bykov^ab

^a Max-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, Germany
^b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

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DOI: https://doi.org/10.4213/tm4081

Abstract: We study flag manifold sigma models that admit a zero-curvature representation. We show that these models can be naturally viewed as interacting (holomorphic and antiholomorphic)

β γ

$\beta \gamma$ -systems. In addition, using the theory of nilpotent orbits of complex Lie groups, we establish a relation of flag manifold sigma models to the principal chiral model.

Funding agency	Grant number
European Research Council	677368
The work is supported in part by the ERC grant in the framework of the European Union “Horizon 2020” program (QUASIFT, grant no. 677368).

Received: October 21, 2019
Revised: January 6, 2020
Accepted: February 11, 2020

English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 309, Pages 78–86
DOI: https://doi.org/10.1134/S0081543820030062

Bibliographic databases:

Document Type: Article

UDC: 514.128+517.972.6+517.958:530.145.83

Language: Russian

Citation: Dmitri V. Bykov, “Flag Manifold Sigma Models and Nilpotent Orbits”, Modern problems of mathematical and theoretical physics, Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov, Trudy Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 89–98; Proc. Steklov Inst. Math., 309 (2020), 78–86

Citation in format AMSBIB

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https://doi.org/10.4213/tm4081

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This publication is cited in the following 12 articles:

Yuki Amari, Toshiaki Fujimori, Muneto Nitta, Keisuke Ohashi, “String junctions in flag manifold sigma models”, Phys. Rev. D, 111:6 (2025)
Toshiaki Fujimori, Muneto Nitta, Keisuke Ohashi, “Moduli spaces of instantons in flag manifold sigma models. Vortices in quiver gauge theories”, J. High Energ. Phys., 2024:2 (2024)
Mikhail Alfimov, Andrey Kurakin, “On bosonic Thirring model in Minkowski signature”, Nuclear Physics B, 998 (2024), 116418
D. V. Bykov, “Sigma models as Gross–Neveu models. II”, Theoret. and Math. Phys., 217:3 (2023), 1842–1854
D. V. Bykov, “Quantum flag manifold $\sigma$ -models and Hermitian Ricci flow”, Comm. Math. Phys., 401 (2023), 1–32
J. Liniado, B. Vicedo, “Integrable degenerate $\mathcal {E}$ -models from $4d$ Chern–Simons theory”, Ann. Henri Poincaré, 24:10 (2023), 3421
S. Lacroix, “Four-dimensional Chern-Simons theory and integrable field theories”, J. Phys. A-Math. Theor., 55:8 (2022), 083001
I. Affleck, D. Bykov, K. Wamer, “Flag manifold SIGMA models: spin chains and integrable theories”, Phys. Rep.-Rev. Sec. Phys. Lett., 953 (2022), 1–93
D. V. Bykov, “Sigma models as Gross–Neveu models”, Theoret. and Math. Phys., 208:2 (2021), 993–1003
Sylvain Lacroix, Benoît Vicedo, “Integrable $\mathcal{E}$ -Models, $4\mathrm{d}$ Chern–Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects”, SIGMA, 17 (2021), 058, 45 pp.
D. Bykov, D. Luest, “Deformed sigma-models, Ricci flow and Toda field theories”, Lett. Math. Phys., 111:6 (2021), 150
V. Caudrelier, M. Stoppato, B. Vicedo, “On the Zakharov-Mikhailov action: 4D Chern-Simons origin and covariant Poisson algebra of the Lax connection”, Lett. Math. Phys., 111:3 (2021), 82

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

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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