AI 中文总结
该研究从等变积分视角统一12维反常框架，将M2、M5、D3膜纳入其中，解释M2/M5对偶性并关联拓扑弦理论的常映射贡献。
AI 中文摘要
我们重新审视长期以来被认为支配M5膜世界体积理论的12维反常多项式，以及近期提出的其对应的D3膜版本。我们证明这些构造自然适配于等变积分框架，使得反常流入公式可完全重写为等变体积的形式。特别地，我们利用如下事实：$S^{2k}$上全局角形式幂次积分的Bott-Cattaneo公式，源于$\boldsymbol{C}^k$的等变欧拉类积分，其中两个副本在球面的南北极反极点粘合。基于此视角，我们将该反常构造推广至包含电荷与磁荷的膜，从而纳入M2膜及D3膜的对偶形式。这为一系列经典结果与近期进展提供了统一框架，并通过类AGT对应自然解释了近期提出的M2/M5对偶性（arXiv:2604.06343），还直接将拓扑弦理论中的常映射贡献重新诠释为M理论反常的体现。
英文摘要
We revisit the twelve-dimensional anomaly polynomial that has long been known to govern M5-brane worldvolume theories, together with its more recently proposed D3-brane counterpart. We show that these constructions naturally fit into the framework of equivariant integration, allowing the anomaly inflow formulas to be rewritten entirely in terms of equivariant volumes. In particular, we use the fact that the Bott--Cattaneo formula for the integral of powers of the global angular form on $S^{2k}$ emerges from the equivariant Euler-class integration of $\mathbb{C}^k$, with two copies glued antipodally at the north and south poles of the sphere. Building on this perspective, we generalize the anomaly construction to include both electrically and magnetically charged branes, thereby incorporating M2-branes as well as a dual formulation of D3-branes. This provides a unified framework encompassing a number of classical results together with several recent developments, and offers a natural interpretation of the recently proposed M2/M5 duality, arxiv:2604.06343, in terms of an AGT-like correspondence. Remarkably, it also leads to a direct reinterpretation of constant-map contributions in topological string theory as manifestations of M-theory anomalies.
Comments35 pages, 2 diagrams
