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arXiv · 2611.06031

Toward Shifted symplectic Chiralization: Deformation of Courant Algebroids

Wenda Fang·Noriaki Ikeda
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Abstract

We study the chiralization of Poisson--Lie theory through graded symplectic geometry. We compare Courant deformations and classical $r$- and $R$-matrix constructions, obtaining integrable hierarchies and free field realizations. We give a variational description of the obstruction to Lie conformal bialgebra compatibility and recover Liberati's obstruction in the Virasoro case. We also introduce a vertex bialgebra analogue of quantized universal enveloping algebras and construct explicit quantizations to all orders of Cartan type Lie conformal bialgebra structures on $\operatorname{Cur}(\mathfrak{sl}_2)$. These results contribute to the first author's broader programme of developing shifted symplectic chiralization as a geometric method for constructing chiral analogues of Poisson-Lie structures via $n$-shifted symplectic geometry, and exploring its connections with AKSZ theory and quantization.

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BibTeXRIS

Wenda Fang, Noriaki Ikeda. 2026-11-04. Toward Shifted symplectic Chiralization: Deformation of Courant Algebroids. https://arxiv.org/abs/2611.06031

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