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Minimal surfaces and weak gravity
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Journal Article
Minimal surfaces and weak gravity
2020
Overview
A
bstract
We show that the Weak Gravity Conjecture (WGC) implies a nontrivial upper bound on the volumes of the minimal-volume cycles in certain homology classes that admit no calibrated representatives. In compactification of type IIB string theory on an orientifold
X
of a Calabi-Yau threefold, we consider a homology class [Σ] ∈
H
4
(
X, ℝ
) represented by a union Σ
∪
of holomorphic and antiholomorphic cycles. The instanton form of the WGC applied to the axion charge [Σ] implies an upper bound on the action of a non-BPS Euclidean D3-brane wrapping the minimal-volume representative Σ
min
of [Σ]. We give an explicit example of an orientifold
X
of a hypersurface in a toric variety, and a hyperplane
H
⊂
H
4
(
X, ℝ
), such that for any [Σ] ∈
H
that satisfies the WGC, the minimal volume obeys Vol (Σ
min
) ≪ Vol(Σ
∪
): the holomorphic and antiholomorphic components recombine to form a much smaller cycle. In particular, the sub-Lattice WGC applied to
X
implies large recombination, no matter how sparse the sublattice. Non-BPS instantons wrapping Σ
min
are then more important than would be predicted from a study of BPS instantons wrapping the separate components of Σ
∪
. Our analysis hinges on a novel computation of effective divisors in
X
that are not inherited from effective divisors of the toric variety.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
