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Minimal surfaces and weak gravity
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DOI：10.1007/JHEP03(2020)021.png)
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Abstract
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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 [sigma] is an element of H-4(X, Double-struck capital R) represented by a union sigma(?) of holomorphic and antiholomorphic cycles. The instanton form of the WGC applied to the axion charge [sigma] implies an upper bound on the action of a non-BPS Euclidean D3-brane wrapping the minimal-volume representative sigma(min) of [sigma]. We give an explicit example of an orientifold X of a hypersurface in a toric variety, and a hyperplane H subset of H-4(X, Double-struck capital R), such that for any [sigma] is an element of H that satisfies the WGC, the minimal volume obeys Vol (sigma(min)) MUCH LESS-THAN Vol(sigma(?)): 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 sigma(min) are then more important than would be predicted from a study of BPS instantons wrapping the separate components of sigma(?). Our analysis hinges on a novel computation of effective divisors in X that are not inherited from effective divisors of the toric variety.
Keywords:
Flux compactifications
D-branes
Solitons Monopoles and Instantons
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