发表机构
University of Guilan（吉兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用扭结de Rham上同调研究D-膜盘积分中Ward恒等式的结构，证明其具有扭结恰当代表元，并确定物理相关的$I/J/K$族张成顶部扭结上同调的五维子空间。
AI 中文摘要
在D-膜上，涉及一个Ramond-Ramond态和两个NSNS态的盘级散射振幅，满足由规范与T-对偶Ward恒等式所施加的标量世界面积分之间的非平凡恒等式。我们利用扭结de Rham上同调研究这些关系的上同调组织，并证明Ward恒等式具有扭结恰当代表元。在$I/J$扇区中，Ward恒等式之间唯一的通用线性相关在同一个扭结de Rham复形中低一度实现，揭示了恒等式及其合冲具有共同的上同调起源。我们还识别了被积函数之间独立的逐点代数关系。独立的上同调秩计算随后确定，物理上选定的$I/J$族在一般复运动学下张成顶部扭结上同调的一个五维子空间。将该构造扩展到$K$族（包括例外双极点代表元$K_3$）不会引入额外的上同调方向。因此，这里考虑的完整$I/J/K$族张成相同的五维子空间。
英文摘要
Disk-level scattering amplitudes involving one Ramond--Ramond and two NSNS states on a D-brane obey nontrivial identities among scalar world-sheet integrals imposed by gauge and T-duality Ward identities. We investigate the cohomological organization of these relations using twisted de Rham cohomology and show that the Ward identities admit twisted-exact representatives. In the $I/J$ sector, the unique generic linear dependence among the Ward identities is realized one degree lower in the same twisted de Rham complex, revealing a common cohomological origin for the identities and their syzygy. We also identify independent pointwise algebraic relations among the integrands. An independent cohomological rank computation then establishes that the physically selected $I/J$ family spans a five-dimensional subspace of the top twisted cohomology at generic complexified kinematics. Extending the construction to the $K$-family, including the exceptional double-pole representative $K_3$, introduces no additional cohomology direction. Hence the complete $I/J/K$ family considered here spans the same five-dimensional subspace.
Comments28 pages
