Minimal Surfaces and Weak Gravity
Jun 19, 2019
Citations per year
Abstract: (Springer)
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(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 of [Σ]. We give an explicit example of an orientifold X of a hypersurface in a toric variety, and a hyperplane H ⊂ H(X, ℝ), such that for any [Σ] ∈ H that satisfies the WGC, the minimal volume obeys Vol (Σ) ≪ 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 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.Note:
- 25 pages
- Flux compactifications
- D-branes
- Solitons Monopoles and Instantons
- instanton: BPS
- surface: minimal
- orientifold
- holomorphic
- homology
- compactification
- recombination
References(52)
Figures(0)
- [6]
- [16]
- [17]
- [22]
- [25]