F-theory on Genus-One Fibrations

Abstract

We argue that M-theory compactified on an arbitrary genus-one fibration, that is, an elliptic fibration which need not have a section, always has an F-theory limit when the area of the genus-one fiber approaches zero. Such genus-one fibrations can be easily constructed as toric hypersurfaces, and various $SU(5)\times U(1{)}^n$ and $E_6$ models are presented as examples. To each genus-one fibration one can associate a $\tau$-function on the base as well as an $SL(2,\mathbb{Z})$ representation which together define the IIB axio-dilaton and 7-brane content of the theory. The set of genus-one fibrations with the same $\tau$-function and $SL(2,\mathbb{Z})$ representation, known as the Tate-Shafarevich group, supplies an important degree of freedom in the corresponding F-theory model which has not been studied carefully until now. Six-dimensional anomaly cancellation as well as Witten's zero-mode count on wrapped branes both imply corrections to the usual F-theory dictionary for some of these models. In particular, neutral hypermultiplets which are localized at codimension-two fibers can arise. (All previous known examples of localized hypermultiplets were charged under the gauge group of the theory.) Finally, in the absence of a section some novel monodromies of Kodaira fibers are allowed which lead to new breaking patterns of non-Abelian gauge groups.

53 pages, 9 figures, 6 tables. v2: references added

References in corpus (2)

• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• 6D supergravity without tensor multiplets

Cited by in corpus (62)

• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Physics of F-theory compactifications without section
• F-theory and the Classification of Little Strings
• Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications
• Yukawas and discrete symmetries in F-theory compactifications without section
• F-Theory Vacua with Z_3 Gauge Symmetry
• 2-Group Symmetries of 6d Little String Theories and T-duality
• Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
• F-theory at order ${\alpha }^{\prime 3}$
• The Global Gauge Group Structure of F-theory Compactification with U(1)s
• Terminal Singularities, Milnor Numbers, and Matter in F-theory
• F-theory and Dark Energy
• Three-Family Particle Physics Models from Global F-theory Compactifications
• Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity
• F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections
• A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
• F-theory and 2d (0,2) Theories
• 6d SCFTs and U(1) Flavour Symmetries
• Fluxes in F-theory Compactifications on Genus-One Fibrations
• F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Gauge Backgrounds and Zero-Mode Counting in F-Theory
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
• Discrete Symmetries in Heterotic/F-theory Duality and Mirror Symmetry
• Generic matter representations in 6D supergravity theories
• An F-theory Realization of the Chiral MSSM with ${\mathbb{Z}}_2$-Parity
• Mordell-Weil Torsion in the Mirror of Multi-Sections
• Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section
• Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17
• Tate's Algorithm for F-theory GUTs with two U(1)s
• Discrete gauge groups in certain F-theory models in six dimensions
• On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
• F-Theory on Quotients of Elliptic Calabi-Yau Threefolds
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
• The Toric SO(10) F-Theory Landscape
• Gauge Groups and Matter Fields on Some Models of F-theory without Section
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Modular Curves and Mordell-Weil Torsion in F-theory
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Non-Abelian discrete gauge symmetries in F-theory
• F-theory duals of singular heterotic K3 mode
• Tools for CICYs in F-theory
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion
• Automatic Enhancement in 6D Supergravity and F-theory Models
• Topological Strings on Non-Commutative Resolutions
• K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications
• Closed tachyon solitons in type II string theory
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces
• Type II String Theory on Calabi-Yau Manifolds with Torsion and Non-Abelian Discrete Gauge Symmetries
• Phenomenology with F-theory SU(5)
• Large U(1) charges from flux breaking in 4D F-theory models
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• The origin of discrete symmetries in F-theory models
• A note on transition in discrete gauge groups in F-theory