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Sigma Models with Complex, Graded and η-Deformed Target Spaces

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Abstract

I describe a class of two-dimensional σ-models with complex homogeneous target spaces, whose equations of motion admit zero-curvature representations. I point out the relation to models with \({{\mathbb{Z}}_{m}}\)-graded target spaces and to the so-called η-deformed models.

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REFERENCES

  1. K. Pohlmeyer, “Integrable Hamiltonian systems and interactions through quadratic constraints,” Commun. Math. Phys. 46, 207 (1976).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. D. Bykov, “Complex structures and zero-curvature equations for \(\sigma \)-models,” Phys. Lett. B 760, 341 (2016).

    Article  ADS  Google Scholar 

  3. C. Klimcik, “Yang–Baxter sigma models and dS/AdS T duality,” JHEP 0212, 051 (2002).

  4. F. Delduc, M. Magro, and B. Vicedo, “An integrable deformation of the \(Ad{{S}_{5}} \times {{S}^{5}}\) superstring action,” Phys. Rev. Lett. 112, 051601 (2014).

    Article  ADS  Google Scholar 

  5. D. Bykov, “Complex structure-induced deformations of σ-models,” JHEP 1703, 130 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. C. A. S. Young, “Non-local charges, Z(m) gradings and coset space actions,” Phys. Lett. B 632, 559–565 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  7. V. G. Kac, “Automorphisms of finite order of semisimple Lie algebras,” Funct. Anal. Appl. 3, 252–254 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Bykov, “Cyclic gradings of Lie algebras and Lax pairs for σ-models,” Theor. Math. Phys. 189, 1734 (2016).

    Article  MathSciNet  MATH  Google Scholar 

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ACKNOWLEDGMENTS

I am grateful to I.Ya. Aref’eva, S. Kuzenko, O. Lechtenfeld, K. Zarembo, P. Zinn-Justin for discussions. I am indebted to Prof. A.A. Slavnov and to my parents for support and encouragement. I would also like to thank E. Ivanov and S. Fedoruk for the invitation to participate in the conference “Supersymmetries and Quantum Symmetries” in Dubna.

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Bykov, D. Sigma Models with Complex, Graded and η-Deformed Target Spaces. Phys. Part. Nuclei 49, 963–965 (2018). https://doi.org/10.1134/S1063779618050131

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  • DOI: https://doi.org/10.1134/S1063779618050131

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