论文标题
T-branes的消失定理
A vanishing theorem for T-branes
论文作者
论文摘要
我们考虑紧凑的复杂歧管上的常规多态希格斯对$（e，ϕ）$。我们表明，h^0（{\ rm end}（e）\ otimes k_s）$限制了流形的ricci曲率，在文献中概括了先前的结果。尤其是$ ϕ $必须消失对于正Ricci曲率，而对于琐碎的规范捆绑包，必须与身份成正比。对于Kähler表面，我们的结果为vafa方程的解决方案提供了新的消失定理。此外，它们在F理论中限制了超对称的7-Brane配置，从而妨碍了T-Branes的存在，即具有$ [ϕ，ϕ^\ Dagger] \ neq 0 $的解决方案。当允许非平凡的希格斯字段时，我们就将其结构的一般表征在矢量束数据方面进行，然后在显式示例中进行说明。
We consider regular polystable Higgs pairs $(E, ϕ)$ on compact complex manifolds. We show that a non-trivial Higgs field $ϕ\in H^0 ({\rm End} (E) \otimes K_S)$ restricts the Ricci curvature of the manifold, generalising previous results in the literature. In particular $ϕ$ must vanish for positive Ricci curvature, while for trivial canonical bundle it must be proportional to the identity. For Kähler surfaces, our results provide a new vanishing theorem for solutions to the Vafa--Witten equations. Moreover they constrain supersymmetric 7-brane configurations in F-theory, giving obstructions to the existence of T-branes, i.e. solutions with $[ϕ, ϕ^\dagger] \neq 0$. When non-trivial Higgs fields are allowed, we give a general characterisation of their structure in terms of vector bundle data, which we then illustrate in explicit examples.
