Are tiny gauge couplings out of the Swampland?

Abstract

There is significant evidence suggesting that continuous global symmetries are always gauged in quantum gravity. However, very weakly gauged symmetries seem global to an effective field theory expansion in powers of Newton's constant. We show that, at least for Einsteinian quantum gravity on AdS, such extremely weak gaugings are indeed in the Swampland: Consistency with AdS black hole thermodynamics requires the bulk gauge coupling $g^2$ not to vanish faster than $\sim \exp ({\ell }^{d-1}/G)$, where $\ell$ is the $Ad{S}_{d+1}$ radius and $G$ is Newton's constant as we take the $G\to 0$ limit. This translates to a constraint in the dual large $N$ CFT, namely, that the two-point function coefficient of the current $C_J$ cannot grow faster than $\exp (N^2)$ in the large $N$ limit. We also recover a previously known logarithmic relationship between the cutoff of the effective field theory in AdS, Planck's mass, and the AdS radius.

arXiv comment22 pages

References in corpus (34)

• The holographic principle
• The String Landscape, Black Holes and Gravity as the Weakest Force
• On the Geometry of the String Landscape and the Swampland
• Causality, Analyticity and an IR Obstruction to UV Completion
• A Covariant Entropy Conjecture
• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Holography from Conformal Field Theory
• The Analytic Bootstrap and AdS Superhorizon Locality
• The Instability of Charged Black Strings and p-Branes
• D=4 Super Yang Mills, D=5 gauged supergravity and D=4 conformal supergravity
• A Natural Language for AdS/CFT Correlators
• Emergent Spacetime and Holographic CFTs
• Super-Planckian Spatial Field Variations and Quantum Gravity
• The Weak Gravity Conjecture and Scalar Fields
• Evidence for a Lattice Weak Gravity Conjecture
• Transplanckian axions !?
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• The Weak Gravity Conjecture in three dimensions
• Natural Inflation and Quantum Gravity
• Planckian Axions and the Weak Gravity Conjecture
• The $\mathcal{N}=2$ superconformal bootstrap
• On the Possibility of Large Axion Moduli Spaces
• Small Hairy Black Holes in $Ad{S}_5\times S^5$
• Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture
• Warping the Weak Gravity Conjecture
• Can Gravitational Instantons Really Constrain Axion Inflation?
• The Exact Superconformal R-symmetry Minimizes ${\tau }_{RR}$
• The Weak Gravity Conjecture and the Axionic Black Hole Paradox
• Massive symmetric tensor field on AdS
• A Chern-Simons Pandemic
• Current Correlators and AdS/CFT Geometry
• What is the Magnetic Weak Gravity Conjecture for Axions?
• An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture

Cited by in corpus (21)

• The Swampland: Introduction and Review
• Infinite Distances in Field Space and Massless Towers of States
• A Stringy Test of the Scalar Weak Gravity Conjecture
• A Tower Weak Gravity Conjecture from Infrared Consistency
• Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter
• The Swampland Distance Conjecture and Towers of Tensionless Branes
• A Holographic Derivation of the Weak Gravity Conjecture
• Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture
• Modular Symmetries and the Swampland Conjectures
• A Strong Scalar Weak Gravity Conjecture and Some Implications
• Complexity is Simple
• A Note on the WGC, Effective Field Theory and Clockwork within String Theory
• The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture
• Bulk Reconstruction in Moduli Space Holography
• AdS-phobia, the WGC, the Standard Model and Supersymmetry
• Pole N-flation
• A Note on 4D Heterotic String Vacua, FI-terms and the Swampland
• A CFT Distance Conjecture
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture