TASI Lectures on F-theory

Abstract

F-theory is perhaps the most general currently available approach to study non-perturbative string compactifications in their geometric, large radius regime. It opens up a wide and ever-growing range of applications and connections to string model building, quantum gravity, (non-perturbative) quantum field theories in various dimensions and mathematics. Its computational power derives from the geometrisation of physical reasoning, establishing a deep correspondence between fundamental concepts in gauge theory and beautiful structures of elliptic fibrations. These lecture notes, which are an extended version of my lectures given at TASI 2017, introduce some of the main concepts underlying the recent technical advances in F-theory compactifications and their various applications. The main focus is put on explaining the F-theory dictionary between the local and global data of an elliptic fibration and the physics of 7-branes in Type IIB compactifications to various dimensions via duality with M-theory. The geometric concepts underlying this dictionary include the behaviour of elliptic fibrations in codimension one, two, three and four, the Mordell-Weil group of rational sections, and the Deligne cohomology group specifying gauge backgrounds.

122 pages

References in corpus (12)

• Classifying bases for 6D F-theory models
• Anomaly Equations and Intersection Theory
• Magnetized E3-brane instantons in F-theory
• New F-theory lifts
• New F-theory lifts II: Permutation orientifolds and enhanced singularities
• New Orientifold Weak Coupling Limits in F-theory
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• Exploring 6D origins of 5D supergravities with Chern-Simons terms
• Algebraic Cycles and Local Anomalies in F-Theory
• Tate Form and Weak Coupling Limits in F-theory

Cited by in corpus (24)

• A Stringy Test of the Scalar Weak Gravity Conjecture
• F-theory and Dark Energy
• On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• General Prescription for Global U(1)'s in 6D SCFTs
• Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity
• Anomaly Inflow Methods for SCFT Constructions in Type IIB
• Discrete gauge groups in certain F-theory models in six dimensions
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• Anomalies as Obstructions: from Dimensional Lifts to Swampland
• Automatic Enhancement in 6D Supergravity and F-theory Models
• On ${\alpha }^{\prime }$-effects from $D$-branes in $4d\mathcal{N}=1$
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• On the LHC signatures of $SU(5)\times U(1{)}^{\prime }$ F-theory motivated models
• Characteristic numbers of elliptic fibrations with non-trivial Mordell-Weil groups
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• Heterotic/Heterotic and Heterotic/F-theory Duality
• Universes as Big Data
• Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi-Yau Three-folds
• Orders of Vanishing and U(1) Charges in F-theory
• Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Moduli Stabilization and Inflation in Type IIB/F-theory