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- Title
A vanishing theorem for T-branes.
- Authors
Marchesano, Fernando; Moraru, Ruxandra; Savelli, Raffaele
- Abstract
We consider regular polystable Higgs pairs (E, ϕ) on compact complex manifolds. We show that a non-trivial Higgs field ϕ ∈ H0(End(E) ⊗ KS) 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†] ≠ 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.
- Subjects
VANISHING theorems; COMPLEX manifolds; VECTOR bundles; VECTOR data; ALGEBRAIC geometry
- Publication
Journal of High Energy Physics, 2020, Vol 2020, Issue 11, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP11(2020)002