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) βγ-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.
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Acknowledgments
I would like to express my sincere gratitude to Andrei Alekseevich Slavnov for his support and warm attitude for many years. I wish him health, cheerfulness, and the pleasure of creative work.
I would like to thank A. Bourget, R. Donagi, S. Frolov, A. Hanany, C. Klimčík, T. McLoughlin, V. Pestun, E. Sharpe, S. Shatashvili, S. Theisen, A. Tseytlin and P. Zinn-Justin for useful discussions, as well as D. Lüst for support. I am grateful to the Institut des hautes études scientifiques (Bures-sur-Yvette, France), where part of this work was done, and in particular to V. Pestun, for hospitality.
Funding
The work is supported in part by the ERC grant in the framework of the European Union “Horizon 2020” program (QUASIFT, grant no. 677368).
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To Andrei Alekseevich Slavnov on the occasion of his 80th birthday with respect and gratitude
This article was submitted by the author simultaneously in Russian and English
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 309, pp. 89–98.
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Bykov, D.V. Flag Manifold Sigma Models and Nilpotent Orbits. Proc. Steklov Inst. Math. 309, 78–86 (2020). https://doi.org/10.1134/S0081543820030062
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DOI: https://doi.org/10.1134/S0081543820030062