A vanishing theorem for T-branes

Abstract

We consider regular polystable Higgs pairs $(E,\varphi )$ on compact complex manifolds. We show that a non-trivial Higgs field $\varphi \in H^0(\mathrm{End}(E)\otimes K_S)$ restricts the Ricci curvature of the manifold, generalising previous results in the literature. In particular $\varphi$ 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 $[\varphi ,{\varphi }^{†}]\ne 0$. 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.

arXiv comment40 pages, 1 grid

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Cited by in corpus (2)

• The Standard Model Quiver in de Sitter String Compactifications
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities