On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
arXiv:1009.5386 · doi:10.1002/prop.201000093
Abstract
We discuss a number of issues arising when computing non-perturbative effects systematically across the string theory landscape. In particular, we cast the study of fairly generic physical properties into the language of computability/number theory and show that this amounts to solving systems of diophantine equations. In analogy to the negative solution to Hilbert's 10th problem, we argue that in such systematic studies there may be no algorithm by which one can determine all physical effects. We take large volume type IIB compactifications as an example, with the physical property of interest being the low-energy non-perturbative F-terms of a generic compactification. A similar analysis is expected to hold for other kinds of string vacua, and we discuss in particular the extension of our ideas to F-theory. While these results imply that it may not be possible to answer systematically certain physical questions about generic type IIB compactifications, we identify particular Calabi-Yau manifolds in which the diophantine equations become linear, and thus can be systematically solved. As part of the study of the required systematics of F-terms, we develop technology for computing Z_2 equivariant line bundle cohomology on toric varieties, which determines the presence of particular instanton zero modes via the Koszul complex. This is of general interest for realistic IIB model building on complete intersections in toric ambient spaces.
arXiv comment52 pages. v2: Added refs, fixed typos
References in corpus (82)
- Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
- Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
- Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications
- Flux Compactification
- Compactifications of F-Theory on Calabi--Yau Threefolds -- I
- Non-Perturbative Superpotentials In String Theory
- Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
- Superstrings and Topological Strings at Large N
- Exact Results for N=2 Compactifications of Heterotic Strings
- GUTs and Exceptional Branes in F-theory - I
- Spacetime Instanton Corrections in 4D String Vacua - The Seesaw Mechanism for D-Brane Models
- GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
- On Geometry and Matrix Models
- Building a Better Racetrack
- Brane Dimers and Quiver Gauge Theories
- Neutrino Majorana Masses from String Theory Instanton Effects
- Mirror Symmetry for Two Parameter Models -- I
- D-brane Instantons in Type II String Theory
- Lectures on F-theory compactifications and model building
- Duality, Monopoles, Dyons, Confinement and Oblique Confinement in Supersymmetric SO(N_c) Gauge Theories
- GUTs in Type IIB Orientifold Compactifications
- Stringy Instantons and Quiver Gauge Theories
- Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds
- Global F-theory GUTs
- Classical gauge instantons from open strings
- Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs
- On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs
- Brane Tilings
- Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra
- Exploring Positive Monad Bundles And A New Heterotic Standard Model
- Non-perturbative Yukawa Couplings from String Instantons
- Computational complexity of the landscape I
- Stringy Instantons at Orbifold Singularities
- Computation of D-brane instanton induced superpotential couplings - Majorana masses from string theory
- Brane Tilings and Their Applications
- D-brane Instantons on the T^6/Z_3 orientifold
- F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds
- Metastable vacua and D-branes at the conifold
- Cohomology of Line Bundles: A Computational Algorithm
- Gauge/gravity duality and meta-stable dynamical supersymmetry breaking
- Non-perturbative and Flux superpotentials for Type I strings on the Z_3 orbifold
- F-theory uplifts and GUTs
- New F-theory lifts
- New F-theory lifts II: Permutation orientifolds and enhanced singularities
- Geometric Transitions and Dynamical SUSY Breaking
- Non-perturbative SQCD Superpotentials from String Instantons
- Instanton Induced Open String Superpotentials and Branes at Singularities
- On Instanton Effects in F-theory
- New Instanton Effects in String Theory
- New Instanton Effects In Supersymmetric QCD
- Local string models of soft supersymmetry breaking
- Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications
- Lifting D-Instanton Zero Modes by Recombination and Background Fluxes
- Dimers and Orientifolds
- Realistic Yukawa Structures from Orientifold Compactifications
- Brane Tilings and Exceptional Collections
- Flux interactions on D-branes and instantons
- Hierarchies from D-brane instantons in globally defined Calabi-Yau Orientifolds
- Neutrino Masses and Mixings from String Theory Instantons
- Non-perturbative F-terms across lines of BPS stability
- Membrane Instantons and de Sitter Vacua
- A Note on G-Fluxes for F-theory Model Building
- String instantons, fluxes and moduli stabilization
- Non-perturbative superpotentials across lines of marginal stability
- The Weinberg Operator and a Lower String Scale in Orientifold Compactifications
- On de Sitter Vacua in Type IIA Orientifold Compactifications
- Stringy Instantons and Yukawa Couplings in MSSM-like Orientifold Models
- Dynamical supersymmetry breaking from unoriented D-brane instantons
- Non-perturbative effective interactions from fluxes
- An Instanton Toolbox for F-Theory Model Building
- D-brane instantons and the effective field theory of flux compactifications
- Stringy instanton corrections to N=2 gauge couplings
- Multi-instanton and string loop corrections in toroidal orbifold models
- Stringy Instanton Effects in Models with Rigid Magnetised D-branes
- On the topology of the hypermultiplet moduli space in type II/CY string vacua
- Branes and instantons at angles and the F-theory lift of O(1) instantons
- Non-perturbative effects and wall-crossing from topological strings
- E3-brane instantons and baryonic operators for D3-branes on toric singularities
- Non-perturbative Vacuum Destabilization and D-brane Dynamics
- Yang-Mills Equations of Motion for the Higgs Sector of SU(3)-Equivariant Quiver Gauge Theories
- D-instanton and polyinstanton effects from type I' D0-brane loops
- D-brane instantons and matrix models
Cited by in corpus (23)
- Models of Particle Physics from Type IIB String Theory and F-theory: A Review
- On the Possibility of Large Axion Moduli Spaces
- Machine Learning in the String Landscape
- Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning
- On Algorithmic Universality in F-theory Compactifications
- A New Construction of Calabi-Yau Manifolds: Generalized CICYs
- An Ultralight Axion in Supersymmetry and Strings and Cosmology at Small Scales
- Computational Complexity of Vacua and Near-Vacua in Field and String Theory
- Topological duality twist and brane instantons in F-theory
- Vacuum Selection from Cosmology on Networks of String Geometries
- Exceptional theories
- Computational Tools for Cohomology of Toric Varieties
- Estimating Calabi-Yau Hypersurface and Triangulation Counts with Equation Learners
- Explore and Exploit with Heterotic Line Bundle Models
- Toric Methods in F-theory Model Building
- Accessibility Measure for Eternal Inflation: Dynamical Criticality and Higgs Metastability
- Statistical Predictions in String Theory and Deep Generative Models
- On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
- Four Kahler Moduli Stabilisation in type IIB Orientifolds with K3-fibred Calabi-Yau threefold compactification
- Undecidable problems in quantum field theory
- Kahler Moduli Stabilization and the Propagation of Decidability
- On finiteness of Type IIB compactifications: Magnetized branes on elliptic Calabi-Yau threefolds
- Constraints on Standard Model Constructions in F-theory