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 -shifted symplectic (QP) data. A Hamiltonian satisfying the classical master equation induces a canonical PVA -bracket, matching the Hamiltonian-operator formalism for integrable hierarchies. As applications, we find the resulting PVA sheaves on and reinterpret our classical -matrix as Maurer-Cartan data in a deformation-theoretic geometric framework, yielding AKS-type integrable hierarchies from the corresponding -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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