Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions

Abstract

We propose quantum gravitational constraints on effective four-dimensional theories with N=1 supersymmetry. These Swampland constraints arise by demanding consistency of the worldsheet theory of a class of axionic, or EFT, strings whose existence follows from the Completeness Conjecture of quantum gravity. Modulo certain assumptions, we derive positivity bounds and quantization conditions for the axionic couplings to the gauge and gravitational sector at the two- and four-derivative level, respectively. We furthermore obtain general bounds on the rank of the gauge sector in terms of the gravitational couplings to the axions. We exemplify how these bounds rule out otherwise consistent effective supergravity theories as theories of quantum gravity. Our derivations of the quantum gravity bounds are tested and further motivated in concrete string theoretic settings. In particular, this leads to a sharper version of the bound on the gauge group rank in F-theory on elliptic four-folds with a smooth base, which improves the known geometrical Kodaira bounds. We furthermore provide a detailed derivation of the EFT string constraints in heterotic string compactifications including higher derivative corrections to the effective action and apply the bounds to M-theory compactifications on $G_2$ manifolds.

84 pages, 2 figures; v2: typos corrected, references added

References in corpus (24)

• On the Geometry of the String Landscape and the Swampland
• Lectures on the Swampland Program in String Compactifications
• Heterotic GUT and Standard Model Vacua from simply connected Calabi-Yau Manifolds
• Global aspects of the space of 6D N = 1 supergravities
• The N=1 effective action of F-theory compactifications
• Positivity of Curvature-Squared Corrections in Gravity
• Moduli Stabilization in Non-Geometric Backgrounds
• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• String Universality and Non-Simply-Connected Gauge Groups in 8d
• 8d Supergravity, Reconstruction of Internal Geometry and the Swampland
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Topological duality twist and brane instantons in F-theory
• Gauge Backgrounds and Zero-Mode Counting in F-Theory
• A landscape of orientifold vacua
• Exploring the landscape of CHL strings on T^d
• The Weak Gravity Conjecture and Axion Strings
• Physics of Infinite Complex Structure Limits in eight Dimensions
• Generic matter representations in 6D supergravity theories
• Tameness, Strings, and the Distance Conjecture
• New Supersymmetric String Theories from Discrete Theta Angles
• 4d strings at strong coupling
• From Rotating to Charged Black Holes and Back Again
• Anomalies as Obstructions: from Dimensional Lifts to Swampland
• Holographic Consistency and the Sign of the Gauss-Bonnet Parameter

Cited by in corpus (7)

• IIB Explored: Reflection 7-Branes
• Finiteness and the Emergence of Dualities
• Towards a complete classification of 6D supergravities
• Light Strings and Strong Coupling in F-theory
• 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
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape