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arXiv · 1909.00742

Ultralocal Lax connection for para-complex $\mathbb{Z}_T$-cosets

Francois Delduc·Takashi Kameyama·Sylvain Lacroix·Marc Magro·Benoit Vicedo
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Abstract

We consider $\sigma$-models on para-complex $\mathbb{Z}_T$-cosets, which are analogues of those on complex homogeneous target spaces considered recently by D. Bykov. For these models, we show the existence of a gauge-invariant Lax connection whose Poisson brackets are ultralocal. Furthermore, its light-cone components commute with one another in the sense of Poisson brackets. This extends a result of O. Brodbeck and M. Zagermann obtained twenty years ago for hermitian symmetric spaces.

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Francois Delduc, Takashi Kameyama, Sylvain Lacroix, Marc Magro, Benoit Vicedo. 2019-09-02. Ultralocal Lax connection for para-complex $\mathbb{Z}_T$-cosets. https://doi.org/10.1016/j.nuclphysb.2019.114821

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