Flat Monodromies and a Moduli Space Size Conjecture

Abstract

We investigate how super-Planckian axions can arise when type IIB 3-form flux is used to restrict a two-axion field space to a one-dimensional winding trajectory. If one does not attempt to address notoriously complicated issues like Kahler moduli stabilization, SUSY-breaking and inflation, this can be done very explicitly. We show that the presence of flux generates flat monodromies in the moduli space which we therefore call 'Monodromic Moduli Space'. While we do indeed find long axionic trajectories, these are non-geodesic. Moreover, the length of geodesics remains highly constrained, in spite of the (finite) monodromy group introduced by the flux. We attempt to formulate this in terms of a 'Moduli Space Size Conjecture'. Interesting mathematical structures arise in that the relevant spaces turn out to be fundamental domains of congruence subgroups of the modular group. In addition, new perspectives on inflation in string theory emerge.

arXiv comment35 pages, 10 figures; v3: references added, new section added

References in corpus (48)

• Axions In String Theory
• The String Landscape, Black Holes and Gravity as the Weakest Force
• On the Geometry of the String Landscape and the Swampland
• Monodromy in the CMB: Gravity Waves and String Inflation
• Gravity Waves and Linear Inflation from Axion Monodromy
• Cosmological Relaxation of the Electroweak Scale
• Completing Natural Inflation
• The String Landscape and the Swampland
• Moduli Stabilization from Fluxes in a Simple IIB Orientifold
• On the Possibility of Large Axion Decay Constants
• Super-Planckian Spatial Field Variations and Quantum Gravity
• The Weak Gravity Conjecture and Scalar Fields
• Transplanckian axions !?
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• F-term Axion Monodromy Inflation
• Backreacted Axion Field Ranges in String Theory
• Natural Inflation and Quantum Gravity
• Planckian Axions and the Weak Gravity Conjecture
• D7-Brane Chaotic Inflation
• Towards Universal Axion Inflation and Reheating in String Theory
• Weak Gravity Strongly Constrains Large-Field Axion Inflation
• The Swampland Conjecture and F-term Axion Monodromy Inflation
• On the Possibility of Large Axion Moduli Spaces
• An Open String Landscape
• The Weak Gravity Conjecture and Effective Field Theory
• Primordial perturbations from inflation with a hyperbolic field-space
• D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
• The Challenge of Realizing F-term Axion Monodromy Inflation in String Theory
• Can Gravitational Instantons Really Constrain Axion Inflation?
• Three-Form Gauging of axion Symmetries and Gravity
• Planckian Axions in String Theory
• The Weak Gravity Conjecture and the Axionic Black Hole Paradox
• What is the Magnetic Weak Gravity Conjecture for Axions?
• Special Points of Inflation in Flux Compactifications
• Quantum Gravity Constraints on Inflation
• Transplanckian Censorship and Global Cosmic Strings
• Natural inflation with and without modulations in type IIB string theory
• Quantum periods of Calabi-Yau fourfolds
• Field dynamics and tunneling in a flux landscape
• A proof of the weak gravity conjecture
• Flux Flattening in Axion Monodromy Inflation
• Conifolds and Tunneling in the String Landscape
• Large Field Inflation and Gravitational Entropy
• The world next door - Results in landscape topography
• A Semiclassical, Entropic Proof of a Weak Gravity Conjecture
• Wormholes and masses for Goldstone bosons
• Restrictions on infinite sequences of type IIB vacua
• On the global moduli of Calabi-Yau threefolds

Cited by in corpus (49)

• The Swampland: Introduction and Review
• Infinite Distances in Field Space and Massless Towers of States
• Emergence and the Swampland Conjectures
• The string swampland constraints require multi-field inflation
• A Tower Weak Gravity Conjecture from Infrared Consistency
• Infinite Distance Networks in Field Space and Charge Orbits
• The Swampland Distance Conjecture for Kahler moduli
• The Weak Gravity Conjecture: A Review
• The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
• A note on Inflation and the Swampland
• The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
• Asymptotic Flux Compactifications and the Swampland
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Instantons and infinite distances
• The Swampland Distance Conjecture and Towers of Tensionless Branes
• Swampland Distance Conjecture, Inflation and $\alpha$-attractors
• Swampland Variations on a Theme by KKLT
• The asymptotic dS Swampland Conjecture - a simplified derivation and a potential loophole
• Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture
• Instanton Corrections and Emergent Strings
• A Geometrical Upper Bound on the Inflaton Range
• Tackling the SDC in AdS with CFTs
• Weakly Coupled de Sitter Vacua with Fluxes and the Swampland
• Classification of discrete modular symmetries in Type IIB flux vacua
• Infinite Distances and the Axion Weak Gravity Conjecture
• What does Inflation say about Dark Energy given the Swampland Conjectures?
• Large Field Inflation/Quintessence and the Refined Swampland Distance Conjecture
• A Tip for Landscape Riders: Multi-Field Inflation Can Fulfill the Swampland Distance Conjecture
• Large Field Ranges from Aligned and Misaligned Winding
• Tameness, Strings, and the Distance Conjecture
• Laplacian spectrum on a nilmanifold, truncations and effective theories
• Inflation, Higher Spins and the Swampland
• Pole N-flation
• De Sitter and Anti-de Sitter branes in self-tuning models
• Transplanckian Censorship and the Local Swampland Distance Conjecture
• Rigid nongeometric orientifolds and the swampland
• $T$-dualizing the de-Sitter no-go scenarios
• Modular Curves and the Refined Distance Conjecture
• A stringy perspective on the coincidence problem
• Modular Inflation at Higher Level $N$
• On the Search for Low $W_0$
• On stable type IIA de-Sitter vacua with geometric flux
• Axion RG flows and the holographic dynamics of instanton densities
• Weak Gravity Conjecture From Low Energy Observers' Perspective
• The self-tuning of the cosmological constant and the holographic relaxion
• The Swampland Spectrum Conjecture in Inflation
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Global aspects of moduli spaces of 2d SCFTs
• Systematic exploration of the non-geometric flux landscape