W=0 Complex Structure Moduli Stabilization on CM-type K3 x K3 Orbifolds:---Arithmetic, Geometry and Particle Physics---
arXiv:2012.01111
Abstract
It is an important question in string compactification whether complex structure moduli stabilization inevitably ends up with a vacuum expectation value of the superpotential < W > of the order of the Planck scale cubed. Any thoughts on volume stabilization and inflation in string theory, as well as on phenomenology of supersymmetric Standard Models, will be affected by the answer to this question. In this work, we follow an idea for making < W > 0 where the internal manifold has a vacuum complex structure with arithmetic characterization, and address Calabi--Yau fourfold compactification of F-theory. The moduli space of K3 x K3 orbifolds contain infinitely many such vacua. Arithmetic conditions for a < W > =0 flux are worked out, and then all the K3 moduli have supersymmetric mass. Possible gauge groups, matter representations and discrete symmetries are studied for the case of Z_2-orbifolds.
arXiv comment70 pages; in v2, reference added and typo corrected; in v3, fixed an error in section 2.2 (v2), and improved understanding on E7-56 matter multiplicity in section 4.3
References in corpus (32)
- Compactifications of F-Theory on Calabi--Yau Threefolds -- II
- M Theory, Orientifolds and G-Flux
- Geometric Singularities and Enhanced Gauge Symmetries
- A New Cohomology Theory for Orbifold
- On Flux Quantization In M-Theory And The Effective Action
- K3 Surfaces and String Duality
- Mirror Manifolds in Higher Dimension
- 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
- Enumerating Flux Vacua with Enhanced Symmetries
- Flavor Structure in F-theory Compactifications
- Les Houches Lectures on Strings and Arithmetic
- Fixing All Moduli for M-Theory on K3xK3
- Branches of the Landscape
- Rational Conformal Field Theories and Complex Multiplication
- Terminal Singularities, Milnor Numbers, and Matter in F-theory
- Fixing D7 Brane Positions by F-Theory Fluxes
- Non-Anomalous Discrete R-symmetry Decrees Three Generations
- Enhanced Symmetries in Multiparameter Flux Vacua
- Supersymmetric Flux Compactifications and Calabi-Yau Modularity
- On the Classification of Elliptic Fibrations modulo Isomorphism on K3 Surfaces with large Picard Number
- Low energy supersymmetry from R-symmetries
- Complex Multiplication for K3 Surfaces
- Automorphisms of K3 surfaces
- Flux Modularity, F-Theory, and Rational Models
- Revisiting arithmetic solutions to the condition
- Classification of non-symplectic automorphisms on K3 surfaces which act trivially on the Néron-Severi lattice
- Calabi-Yau 4-folds of Borcea--Voisin type from F-Theory
- Classification of order sixteen non-symplectic automorphisms on K3 surfaces
- The modularity of K3 surfaces with non-symplectic group actions
- Real multiplication on K3 surfaces and Kuga Satake varieties