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arXiv · 1508.05832

$η$ and $λ$ deformations as ${\cal E}$-models

Ctirad Klimcik
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Abstract

We show that the so called $λ$ deformed $σ$-model as well as the $η$ deformed one belong to a class of the ${\cal E}$-models introduced in the context of the Poisson-Lie-T-duality. The $λ$ and $η$ theories differ solely by the choice of the Drinfeld double; for the $λ$ model the double is the direct product $G\times G$ while for the $η$ model it is the complexified group $G^{\mathbb{C}}$. As a consequence of this picture, we prove for any $G$ that the target space geometries of the $λ$-model and of the Poisson-Lie T-dual of the $η$-model are related by a simple analytic continuation.

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Ctirad Klimcik. 2015-09-21. $η$ and $λ$ deformations as ${\cal E}$-models. https://doi.org/10.1016/j.nuclphysb.2015.09.011

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