Minimal Surfaces and Weak Gravity

Jun 19, 2019
26 pages
Published in:
  • JHEP 03 (2020) 021
  • Published: Mar 4, 2020
e-Print:

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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] ∈ H4_{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 Σmin_{min} of [Σ]. We give an explicit example of an orientifold X of a hypersurface in a toric variety, and a hyperplane H ⊂ H4_{4}(X, ℝ), such that for any [Σ] ∈ H that satisfies the WGC, the minimal volume obeys Vol (Σmin_{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 Σmin_{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.
Note:
  • 25 pages
  • Flux compactifications
  • D-branes
  • Solitons Monopoles and Instantons
  • instanton: BPS
  • surface: minimal
  • orientifold
  • holomorphic
  • homology
  • compactification
  • recombination