Minimal Surfaces and Weak Gravity

Abstract

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 ${\Sigma }_{\min }$ 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 $\mathrm{Vol}({\Sigma }_{\min })\ll \mathrm{Vol}({\Sigma }_{\cup })$: 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 ${\Sigma }_{\min }$ 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.

arXiv comment25 pages

References in corpus (27)

• The String Landscape, Black Holes and Gravity as the Weakest Force
• Non-Perturbative Superpotentials In String Theory
• Infinite Distances in Field Space and Massless Towers of States
• Nonlinear Instantons from Supersymmetric p-Branes
• D-brane Instantons in Type II String Theory
• Tensionless Strings and the Weak Gravity Conjecture
• Naturalness and the Weak Gravity Conjecture
• The Weak Gravity Conjecture and Scalar Fields
• Evidence for a Lattice Weak Gravity Conjecture
• Emergence and the Swampland Conjectures
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• Weak Gravity Conjecture from Unitarity and Causality
• A Stringy Test of the Scalar Weak Gravity Conjecture
• The Weak Gravity Conjecture in three dimensions
• Proof of the Weak Gravity Conjecture from Black Hole Entropy
• A Tower Weak Gravity Conjecture from Infrared Consistency
• The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
• Cohomology of Line Bundles: A Computational Algorithm
• Constraints on Axion Inflation from the Weak Gravity Conjecture
• New F-theory lifts
• New F-theory lifts II: Permutation orientifolds and enhanced singularities
• New Instanton Effects in String Theory
• Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape
• Non-perturbative F-terms across lines of BPS stability
• SUSY breaking mediation by D-brane instantons
• (Non-)BPS bound states and D-brane instantons
• Euler Characteristics of Crepant Resolutions of Weierstrass Models

Cited by in corpus (14)

• The Weak Gravity Conjecture: A Review
• Superradiance in String Theory
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• PQ Axiverse
• Duality and Axionic Weak Gravity
• Fuzzy Dark Matter Candidates from String Theory
• Weak Gravity Bounds in Asymptotic String Compactifications
• Moduli Space Reconstruction and Weak Gravity
• Non-Holomorphic Cycles and Non-BPS Black Branes
• Superpotentials from Singular Divisors
• Constraints on Standard Model Constructions in F-theory
• Instanton Resummation and the Weak Gravity Conjecture
• Decay channels for double extremal black holes in four dimensions
• Constraining the inflaton potential with gravitational waves from oscillons