Root Bundles and Towards Exact Matter Spectra of F-theory MSSMs
arXiv:2102.10115 · doi:10.1007/JHEP09(2021)076
Abstract
Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundles and can be thought of as generalizations of spin bundles. We explain how these root bundles are linked to inequivalent F-theory gauge potentials of a -flux. While this observation is interesting in its own right, it is particularly valuable for F-theory Standard Model constructions. In aiming for MSSMs, it is desired to argue for the absence of vector-like exotics. We work out the root bundle constraints on all matter curves in the largest class of currently-known F-theory Standard Model constructions without chiral exotics and gauge coupling unification. On each matter curve, we conduct a systematic "bottom"-analysis of all solutions to the root bundle constraints and all spin bundles. Thereby, we derive a lower bound for the number of combinations of root bundles and spin bundles whose cohomologies satisfy the physical demand of absence of vector-like pairs. On a technical level, this systematic study is achieved by a well-known diagrammatic description of root bundles on nodal curves. We extend this description by a counting procedure, which determines the cohomologies of so-called limit root bundles on full blow-ups of nodal curves. By use of deformation theory, these results constrain the vector-like spectra on the smooth matter curves in the actual F-theory geometry.
arXiv comment38 pages + appendix
References in corpus (51)
- Evidence for F-Theory
- Compactifications of F-Theory on Calabi--Yau Threefolds -- II
- Compactifications of F-Theory on Calabi--Yau Threefolds -- I
- Branes Intersecting at Angles
- Toward Realistic Intersecting D-Brane Models
- On Flux Quantization In M-Theory And The Effective Action
- Chiral Four-Dimensional N=1 Supersymmetric Type IIA Orientifolds from Intersecting D6-Branes
- GUTs and Exceptional Branes in F-theory - I
- Three-Family Supersymmetric Standard-like Models from Intersecting Brane Worlds
- Intersecting Brane Worlds
- D=4 Chiral String Compactifications from Intersecting Branes
- Getting just the Standard Model at Intersecting Branes
- An SU(5) Heterotic Standard Model
- A Heterotic Standard Model
- The Standard Model from Stable Intersecting Brane World Orbifolds
- Heterotic Line Bundle Standard Models
- F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
- New Aspects of Heterotic--F Theory Duality
- F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
- Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds
- Particle Physics Implications of F-theory
- Exploring Positive Monad Bundles And A New Heterotic Standard Model
- Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
- G-flux in F-theory and algebraic cycles
- G_4 flux, chiral matter and singularity resolution in F-theory compactifications
- F-theory fluxes, Chirality and Chern-Simons theories
- Anomaly Equations and Intersection Theory
- Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
- Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors
- Tri-linear Couplings in an Heterotic Minimal Supersymmetric Standard Model
- Gauge Fluxes in F-theory and Type IIB Orientifolds
- Three-Family Particle Physics Models from Global F-theory Compactifications
- On Flux Quantization in F-Theory
- A Quadrillion Standard Models from F-theory
- Conifold Transitions in M-theory on Calabi-Yau Fourfolds with Background Fluxes
- G4-Flux and Standard Model Vacua in F-theory
- Fluxes in F-theory Compactifications on Genus-One Fibrations
- Gauge Backgrounds and Zero-Mode Counting in F-Theory
- Chow groups, Deligne cohomology and massless matter in F-theory
- On heterotic model constraints
- An F-theory Realization of the Chiral MSSM with -Parity
- Calabi-Yau Volumes and Reflexive Polytopes
- The Picard Group of the Moduli of Higher Spin Curves
- Machine Learning and Algebraic Approaches towards Complete Matter Spectra in 4d F-theory
- Constraining the Kahler Moduli in the Heterotic Standard Model
- Three-form periods on Calabi-Yau fourfolds: Toric hypersurfaces and F-theory applications
- The Prym-Green Conjecture for torsion bundles of high order
- Cohomologies of coherent sheaves and massless spectra in F-theory
- Vector-Like Pairs and Brill--Noether Theory
- On Mirror Symmetry for Calabi-Yau Fourfolds with Three-Form Cohomology
- Combinatorial aspects of nodal curves