AI 中文总结
本文研究黎曼面主圆周丛上含联络与B-场的混合场几何，引入扭曲Yang-Mills泛函，构造模空间并证明其为Heisenberg接触流形，揭示T-对偶对泛函的保持性及在λ=1时诱导模空间的对合接触同胚。
AI 中文摘要
我们从规范理论与T-对偶的视角，研究黎曼面上主圆周丛上由联络与B-场构成的混合场的几何性质。受Atiyah--Bott与Segal奠基性工作的启发，我们引入了一种扭曲Yang--Mills泛函，其在平坦情形下的临界轨迹由曲率与H-通量的同时消失所支配。我们证明规范群是由整数λ参数化的阿贝尔群的半直积。模空间通过预辛约化构造得到，且在λ≠0时为Heisenberg接触流形，我们完全刻画了其拓扑性质。我们证明T-对偶保持扭曲Yang--Mills泛函，并作用于平坦混合场的构型空间。我们确定了与T-对偶映射相容的规范变换子群，并描述了其在可T-对偶化平坦混合场的奇异商空间上的诱导作用。恰好在λ=1时，T-对偶下延为模空间上的对合接触同胚。
英文摘要
We study the geometry of mixed fields, consisting of a connection and a $B$-field on a principal circle bundle over a Riemann surface, from the perspective of gauge theory and T-duality. Motivated by the foundational work of Atiyah--Bott and Segal, we introduce a twisted Yang--Mills functional whose critical locus, in the flat case, is governed by the simultaneous vanishing of the curvature and the $H$-flux. We show that the gauge group is a semi-direct product of abelian groups parametrised by an integer $λ$. The moduli spaces are constructed by presymplectic reduction and shown to be Heisenberg contact manifolds for $λ\neq 0$, whose topology we characterise completely. We show that T-duality preserves the twisted Yang--Mills functional and acts on the configuration space of flat mixed fields. We identify the subgroups of gauge transformations that are compatible with the T-duality map and describe the induced action on the singular quotient of T-dualizable flat mixed fields. Precisely at $λ=1$ does T-duality descend to an involutive contactomorphism of the moduli space.
Comments39 pages
