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.
Similar content being viewed by others
REFERENCES
K. Pohlmeyer, “Integrable Hamiltonian systems and interactions through quadratic constraints,” Commun. Math. Phys. 46, 207 (1976).
D. Bykov, “Complex structures and zero-curvature equations for \(\sigma \)-models,” Phys. Lett. B 760, 341 (2016).
C. Klimcik, “Yang–Baxter sigma models and dS/AdS T duality,” JHEP 0212, 051 (2002).
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).
D. Bykov, “Complex structure-induced deformations of σ-models,” JHEP 1703, 130 (2017).
C. A. S. Young, “Non-local charges, Z(m) gradings and coset space actions,” Phys. Lett. B 632, 559–565 (2006).
V. G. Kac, “Automorphisms of finite order of semisimple Lie algebras,” Funct. Anal. Appl. 3, 252–254 (1969).
D. Bykov, “Cyclic gradings of Lie algebras and Lax pairs for σ-models,” Theor. Math. Phys. 189, 1734 (2016).
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
1The article is published in the original.
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779618050131