Toward Shifted symplectic Chiralization: Deformation of Courant Algebroids

@misc{fang2026toward,
  title = {{Toward Shifted symplectic Chiralization: Deformation of Courant Algebroids}},
  author = {Wenda Fang and Noriaki Ikeda},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06031},
  eprint = {2611.06031},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06031},
}

TY  - UNPB
TI  - Toward Shifted symplectic Chiralization: Deformation of Courant Algebroids
AU  - Wenda Fang
AU  - Noriaki Ikeda
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06031
UR  - https://arxiv.org/abs/2611.06031
AB  - 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 Cur(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.
ER  -