AI 中文总结
该研究从微分泊松几何出发，将微分泊松西格玛模型（DPSM）的经典约化定义为辛靶流形上的A型模型，揭示了A型模型曲率耦合的一阶泊松起源，还给出了该类模型的实例与排除情形。
AI 中文摘要
我们研究辛情形下的微分泊松西格玛模型（DPSM），并证明其经典约化定义了辛靶流形上的一类特殊A型模型，该类模型不一定是凯勒型的。DPSM是一种协变一阶西格玛模型，其分次靶流形是泊松流形M的平移切丛T[1]M。其分次泊松张量编码了C(T[1]M)≅Ω^•(M)上的微分泊松括号，该括号以协变形式用联络Γ及其转置Γ̃表示。在非退化情形下，雅可比恒等式要求Γ是平坦的，而约化作用的四次耦合由Γ̃的曲率给出，该曲率由Γ的挠率诱导。因此，DPSM选出了一类辛类，其中A型模型的曲率耦合具有一阶泊松起源。我们通过例子和障碍来描述这类辛类：复射影空间CP^n和K3曲面被排除在外，而仿射辛靶流形、辛环面以及Kodaira-Thurston流形提供了明确的例子。T[1]M上的分次父几何为Ω^•(M)配备了微分泊松括号，并为Ω^•(M)[1]配备了严格的L_∞代数结构，这为 observable 复形赋予了自然的链级微分泊松结构，而该结构在A型模型通常的凯勒表述中并不明显。
英文摘要
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 graded Poisson algebra structure; in particular, the underlying differential graded Lie algebra defines a strict $L_\infty$-algebra on the observable complex. This chain-level structure is not manifest in the usual Kähler formulation of the A-model.
Commentsv2: corrected the grading/sign conventions for the differential Poisson bracket on forms, streamlined the observable-algebra discussion, and fixed minor typos
