A-type Sigma Models from Differential Poisson Geometry

Engineering notes

Engineering notes will be added by the Power for Solar editorial team.

Chinese explanation / 中文解读

中文解读待补充：本站会优先为光伏效率、钙钛矿太阳能电池、储能技术、太阳能热利用、BIPV、并网技术等高价值论文补充中文说明。

Original abstract

We study the differential Poisson sigma model (DPSM) in the symplectic case and show that its classical reduction defines a distinguished class of A-type models on symplectic targets, not necessarily Kähler. The DPSM is a covariant first-order sigma model whose graded target is the parity-shifted tangent bundle $T[1]M$ of a Poisson manifold $M$. Its graded Poisson tensor encodes a differential Poisson bracket on $C(T[1]M)\congΩ^\bullet(M)$, written covariantly in terms of a connection $Γ$ and its transpose $\widetildeΓ$. In the nondegenerate case, the Jacobi identities force $Γ$ to be flat, while the quartic coupling of the reduced action is given by the curvature of $\widetildeΓ$, induced by the torsion of $Γ$. Thus, the DPSM selects a symplectic class in which the A-model curvature coupling acquires a first-order Poisson origin. We describe this class through examples and obstructions; $\mathbb{CP}^n$ and K3 surfaces are excluded, while affine symplectic targets, symplectic tori, and the Kodaira--Thurston manifold furnish explicit examples. The graded parent geometry on $T[1]M$ equips $Ω^\bullet(M)$ with a differential Poisson bracket and $Ω^\bullet(M)[1]$ with a strict $L_\infty$-algebra structure, equipping the observable complex with a natural chain-level differential Poisson structure that is not manifest in the usual Kähler formulation of the A-model.

Links and sources

• Official / arXiv page
• PDF from original source

Comments