English

Shifted symplectic structures and Poisson vertex algebra

Quantum Algebra 2026-01-27 v1 Mathematical Physics math.MP Representation Theory Symplectic Geometry

Abstract

We construct Poisson vertex algebra (PVA) structures on arc spaces from 11-shifted symplectic (QP) data. A Hamiltonian satisfying the classical master equation induces a canonical PVA λ\lambda-bracket, matching the Hamiltonian-operator formalism for integrable hierarchies. As applications, we find the resulting PVA sheaves on P1\mathbb P^1 and reinterpret our classical RR-matrix as Maurer-Cartan data in a deformation-theoretic geometric framework, yielding AKS-type integrable hierarchies from the corresponding RR-deformations.

Keywords

Cite

@article{arxiv.2601.17840,
  title  = {Shifted symplectic structures and Poisson vertex algebra},
  author = {Wenda Fang},
  journal= {arXiv preprint arXiv:2601.17840},
  year   = {2026}
}

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R2 v1 2026-07-01T09:19:11.221Z