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arXiv · 2309.13413

Integrable sigma models with complex and generalized complex structures

A. Rezaei-Aghdam·A. Taghavi
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Abstract

Using the general method presented by Mohammedi \cite{NM} for the integrability of a sigma model on a manifold, we investigate the conditions for having an integrable deformation of the general sigma model on a manifold with a complex structure. On a Lie group, these conditions are satisfied by using the zeros of the Nijenhuis tensor. We then extend this formalism to a manifold, especially a Lie group, with a generalized complex structure. We demonstrate that, for the examples of integrable sigma models with generalized complex structures on the Lie groups $\mathbf{A_{4,8}}$ and $\mathbf{A_{4,10}}$, under special conditions, the perturbed terms of the actions are identical to the WZ terms.

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A. Rezaei-Aghdam, A. Taghavi. 2023-09-23. Integrable sigma models with complex and generalized complex structures. https://doi.org/10.1016/j.geomphys.2025.105527

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