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تسجيل مستخدم جديدMinimal Surfaces and Weak Gravity
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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 $[Sigma] in H_4(X,mathbb{Z})$ represented by a union $Sigma_{cup}$ 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 $Sigma_{mathrm{min}}$ of $[Sigma]$. We give an explicit example of an orientifold $X$ of a hypersurface in a toric variety, and a hyperplane $mathcal{H} subset H_4(X,mathbb{Z})$, such that for any $[Sigma] in H$ that satisfies the WGC, the minimal volume obeys $mathrm{Vol}(Sigma_{mathrm{min}}) ll mathrm{Vol}(Sigma_{cup})$: 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 $Sigma_{mathrm{min}}$ are then more important than would be predicted from a study of BPS instantons wrapping the separate components of $Sigma_{cup}$. Our analysis hinges on a novel computation of effective divisors in $X$ that are not inherited from effective divisors of the toric variety.
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