Infinite Distance Networks in Field Space and Charge Orbits

Abstract

The Swampland Distance Conjecture proposes that approaching infinite distances in field space an infinite tower of states becomes exponentially light. We study this conjecture for the complex structure moduli space of Calabi-Yau manifolds. In this context, we uncover significant structure within the proposal by showing that there is a rich spectrum of different infinite distance loci that can be classified by certain topological data derived from an associated discrete symmetry. We show how this data also determines the rules for how the different infinite distance loci can intersect and form an infinite distance network. We study the properties of the intersections in detail and, in particular, propose an identification of the infinite tower of states near such intersections in terms of what we term charge orbits. These orbits have the property that they are not completely local, but depend on data within a finite patch around the intersection, thereby forming an initial step towards understanding global aspects of the distance conjecture in field spaces. Our results follow from a deep mathematical structure captured by the so-called orbit theorems, which gives a handle on singularities in the moduli space through mixed Hodge structures, and is related to a local notion of mirror symmetry thereby allowing us to apply it also to the large volume setting. These theorems are general and apply far beyond Calabi-Yau moduli spaces, leading us to propose that similarly the infinite distance structures we uncover are also more general.

arXiv comment81 pages, 20 figures. v2: Expanded discussions, fixed typos and added references. v3: Typos corrected, published version

References in corpus (23)

• On the Geometry of the String Landscape and the Swampland
• Distance and de Sitter Conjectures on the Swampland
• N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map
• Mirror Symmetry for Two Parameter Models -- II
• Infinite Distances in Field Space and Massless Towers of States
• Mirror Symmetry for Two Parameter Models -- I
• Tensionless Strings and the Weak Gravity Conjecture
• Super-Planckian Spatial Field Variations and Quantum Gravity
• The Weak Gravity Conjecture and Scalar Fields
• Emergence and the Swampland Conjectures
• A Stringy Test of the Scalar Weak Gravity Conjecture
• Backreacted Axion Field Ranges in String Theory
• The Swampland Conjecture and F-term Axion Monodromy Inflation
• What is Special Kähler Geometry ?
• The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
• Backreaction Issues in Axion Monodromy and Minkowski 4-forms
• Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture
• A Geometrical Upper Bound on the Inflaton Range
• Flat Monodromies and a Moduli Space Size Conjecture
• Quantum Cohomology and Periods
• The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies
• Mass Hierarchies and Dynamical Field Range
• Quantum periods of Calabi-Yau fourfolds

Cited by in corpus (86)

• Lectures on the Swampland Program in String Compactifications
• AdS and the Swampland
• The Swampland Distance Conjecture for Kahler moduli
• The Weak Gravity Conjecture: A Review
• The web of swampland conjectures and the TCC bound
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Asymptotic Flux Compactifications and the Swampland
• Repulsive Forces and the Weak Gravity Conjecture
• Swampland Conjectures for Strings and Membranes
• Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter
• Instantons and infinite distances
• The Swampland Distance Conjecture and Towers of Tensionless Branes
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• Swampland Distance Conjecture, Inflation and $\alpha$-attractors
• A Holographic Derivation of the Weak Gravity Conjecture
• Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture
• Swampland Variations on a Theme by KKLT
• Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds
• Gaugino condensation and small uplifts in KKLT
• Sharpening the Distance Conjecture in Diverse Dimensions
• Instanton Corrections and Emergent Strings
• The Emergence Proposal in Quantum Gravity and the Species Scale
• Tackling the SDC in AdS with CFTs
• The Convex Hull Swampland Distance Conjecture and Bounds on Non-geodesics
• Modular Symmetries and the Swampland Conjectures
• Weakly Coupled de Sitter Vacua with Fluxes and the Swampland
• A Gravitino Distance Conjecture
• A Strong Scalar Weak Gravity Conjecture and Some Implications
• de Sitter in non-supersymmetric string theories: no-go theorems and brane-worlds
• Moduli Space Holography and the Finiteness of Flux Vacua
• EFT strings and emergence
• Weak Gravity Bounds in Asymptotic String Compactifications
• Moduli Stabilization in Asymptotic Flux Compactifications
• The trans-Planckian censorship conjecture from the swampland distance conjecture
• Asymptotic Accelerated Expansion in String Theory and the Swampland
• Infinite Distances and the Axion Weak Gravity Conjecture
• Asymptotic Observables and the Swampland
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Infinite Black Hole Entropies at Infinite Distances and Tower of States
• Special Geometry and the Swampland
• The Weak Gravity Conjecture and Axion Strings
• Refined swampland distance conjecture and exotic hybrid Calabi-Yaus
• Physics of Infinite Complex Structure Limits in eight Dimensions
• On TCS $G_2$ manifolds and 4D Emergent Strings
• Swampland, Gradient Flow and Infinite Distance
• Membrane Limits in Quantum Gravity
• Bulk Reconstruction in Moduli Space Holography
• Thraxions: Ultralight Throat Axions
• Relating the scalar weak gravity conjecture and the swampland distance conjecture for an accelerating universe
• Large Field Ranges from Aligned and Misaligned Winding
• de Sitter Space as a Glauber-Sudarshan State
• Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models
• Tameness, Strings, and the Distance Conjecture
• Small Black Hole Explosions
• Fermions and the Swampland
• 4d strings at strong coupling
• Moduli Space Reconstruction and Weak Gravity
• Role of trans-Planckian modes in cosmology
• Universal Axion Backreaction in Flux Compactifications
• Rigid nongeometric orientifolds and the swampland
• Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• $T$-dualizing the de-Sitter no-go scenarios
• Finiteness and the Emergence of Dualities
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Infinite Distance and Zero Gauge Coupling in 5d Supergravity
• Remarks on the effects of quantum corrections on moduli stabilization and de Sitter vacua in type IIB string theory
• Weak $G_2$-manifolds and scale separation in M-theory from type IIA backgrounds
• Conifold dynamics and axion monodromies
• On stable type IIA de-Sitter vacua with geometric flux
• Swampland geometry and the gauge couplings
• A CFT Distance Conjecture
• Emergent Strings in Type IIB Calabi--Yau Compactifications
• The Fate of Discrete 1-Form Symmetries in 6d
• Deformed WZW Models and Hodge Theory -- Part I
• Seeking de-Sitter Vacua in the String Landscape
• Consistency of Cubic Galileon Cosmology: Model-Independent Bounds from Background Expansion and Perturbative Analyses
• A Note on the Swampland Distance Conjecture
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Stability of BPS States and Weak Coupling Limits
• Bounds on complex structure moduli values for perturbative control
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories
• The Tadpole Conjecture in Asymptotic Limits
• Systematic exploration of the non-geometric flux landscape