skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The F-theory geometry with most flux vacua

Abstract

Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold Mmax gives rise to O(10272,000) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O(10–3000). The fourfold Mmax arises from a generic elliptic fibration over a specific toric threefold base Bmax, and gives a geometrically non-Higgsable gauge group of E89 × F48 × (G 2 × SU(2))16, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in Mmax, or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E8 factor. Furthermore, the results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on Mmax.

Authors:
 [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1237042
Grant/Contract Number:  
SC0012567
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; flux compactifications; F-Theory; superstring vacua

Citation Formats

Taylor, Washington, and Wang, Yi -Nan. The F-theory geometry with most flux vacua. United States: N. p., 2015. Web. https://doi.org/10.1007/JHEP12(2015)164.
Taylor, Washington, & Wang, Yi -Nan. The F-theory geometry with most flux vacua. United States. https://doi.org/10.1007/JHEP12(2015)164
Taylor, Washington, and Wang, Yi -Nan. Mon . "The F-theory geometry with most flux vacua". United States. https://doi.org/10.1007/JHEP12(2015)164. https://www.osti.gov/servlets/purl/1237042.
@article{osti_1237042,
title = {The F-theory geometry with most flux vacua},
author = {Taylor, Washington and Wang, Yi -Nan},
abstractNote = {Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold Mmax gives rise to O(10272,000) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O(10–3000). The fourfold Mmax arises from a generic elliptic fibration over a specific toric threefold base Bmax, and gives a geometrically non-Higgsable gauge group of E89 × F48 × (G 2 × SU(2))16, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in Mmax, or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E8 factor. Furthermore, the results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on Mmax.},
doi = {10.1007/JHEP12(2015)164},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2015,
place = {United States},
year = {2015},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 8 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Landau-Ginzburg vacua of string, M- and F-theory at c=12
journal, June 1999


Breaking GUT groups in F-theory
journal, January 2011


ℙ 1 $$ {\mathrm{\mathbb{P}}}^1 $$ -bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models
journal, September 2015

  • Halverson, James; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/jhep09(2015)086

hypersurfaces in algebraic tori
journal, February 1993


Calabi-Yau 4-folds and toric fibrations
journal, July 1998


Geometric constraints in dual F-theory and heterotic string compactifications
journal, August 2014

  • Anderson, Lara B.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/jhep08(2014)025

The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications
journal, January 2015


The Geometry of Toric Varieties
journal, April 1978


Compactifications of F-theory on Calabi-Yau threefolds (II)
journal, September 1996


Non-Higgsable QCD and the standard model spectrum in F-theory
journal, January 2015

  • Grassi, Antonella; Halverson, James; Shaneson, Julius
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/jhep01(2015)086

Geometric singularities and enhanced gauge symmetries
journal, December 1996


On the classification of 6D SCFTs and generalized ADE orbifolds
journal, May 2014

  • Heckman, Jonathan J.; Morrison, David R.; Vafa, Cumrun
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/jhep05(2014)028

6D SCFTs and gravity
journal, June 2015

  • Del Zotto, Michele; Heckman, Jonathan J.; Morrison, David R.
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/jhep06(2015)158

On minimal models of elliptic threefolds
journal, March 1991


Evidence for F-theory
journal, June 1996


Atomic classification of 6D SCFTs: Atomic classification of 6D SCFTs
journal, June 2015

  • Heckman, Jonathan J.; Morrison, David R.; Rudelius, Tom
  • Fortschritte der Physik, Vol. 63, Issue 7-8
  • DOI: 10.1002/prop.201500024

Compactifications of F-theory on Calabi-Yau threefolds. (I)
journal, August 1996


Statistics of F-theory flux vacua for particle physics
journal, November 2015


GUTs and exceptional branes in F-theory — II. Experimental predictions
journal, January 2009


GUTs and exceptional branes in F-theory — I
journal, January 2009


G-flux in F-theory and algebraic cycles
journal, March 2012


On the Hodge structure of elliptically fibered Calabi-Yau threefolds
journal, August 2012


Calabi-Yau threefolds with large h 2,1
journal, October 2014

  • Johnson, Samuel B.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/jhep10(2014)023

F-theory, SO(32) and toric geometry
journal, November 1997


The statistics of string/M theory vacua
journal, May 2003


Non-Higgsable clusters for 4D F-theory models
journal, May 2015

  • Morrison, David R.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/jhep05(2015)080

Quantization of four-form fluxes and dynamical neutralization of the cosmological constant
journal, May 2000


Flux compactification
journal, May 2007


Computing brane and flux superpotentials in F-theory compactifications
journal, April 2010

  • Grimm, Thomas W.; Ha, Tae-Won; Klemm, Albrecht
  • Journal of High Energy Physics, Vol. 2010, Issue 4
  • DOI: 10.1007/jhep04(2010)015

Lattice points in high-dimensional spheres
journal, March 1990

  • Mazo, J. E.; Odlyzko, A. M.
  • Monatshefte für Mathematik, Vol. 110, Issue 1
  • DOI: 10.1007/bf01571276

Anthropic Bound on the Cosmological Constant
journal, November 1987


6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
journal, June 2015

  • Martini, Gabriella; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/jhep06(2015)061

Calabi-Yau four-folds for M- and F-theory compactifications
journal, May 1998


Toric geometry and enhanced gauge symmetry of F-theory/heterotic vacua
journal, December 1997


Counting Flux Vacua
journal, January 2004


Distributions of flux vacua
journal, May 2004


NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: COSMOLOGICAL PARAMETER RESULTS
journal, September 2013

  • Hinshaw, G.; Larson, D.; Komatsu, E.
  • The Astrophysical Journal Supplement Series, Vol. 208, Issue 2
  • DOI: 10.1088/0067-0049/208/2/19

Complete classification of reflexive polyhedra in four dimensions
journal, January 2000

  • Kreuzer, Maximilian; Skarke, Harald
  • Advances in Theoretical and Mathematical Physics, Vol. 4, Issue 6
  • DOI: 10.4310/atmp.2000.v4.n6.a2

Toric bases for 6D F-theory models
journal, May 2012


Flux compactifications in string theory: A comprehensive review
journal, January 2006


Anthropic Bound on the Cosmological Constant
journal, November 1987


Flux compactification
journal, May 2007


Toric geometry and enhanced gauge symmetry of F-theory/heterotic vacua
journal, December 1997


Landau-Ginzburg vacua of string, M- and F-theory at c=12
journal, June 1999


Geometric constraints in dual F-theory and heterotic string compactifications
journal, August 2014

  • Anderson, Lara B.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)025

Non-Higgsable QCD and the standard model spectrum in F-theory
journal, January 2015

  • Grassi, Antonella; Halverson, James; Shaneson, Julius
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)086

Non-Higgsable clusters for 4D F-theory models
journal, May 2015

  • Morrison, David R.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)080

ℙ 1 $$ {\mathrm{\mathbb{P}}}^1 $$ -bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models
journal, September 2015

  • Halverson, James; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)086

On the Hodge structure of elliptically fibered Calabi-Yau threefolds
journal, August 2012


The Geometry of Toric Varieties
journal, April 1978


F-theory, SO(32) and toric geometry
journal, November 1997


6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
journal, June 2015

  • Martini, Gabriella; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)061

Calabi-Yau threefolds with large h 2,1
journal, October 2014

  • Johnson, Samuel B.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)023

On the classification of 6D SCFTs and generalized ADE orbifolds
journal, May 2014

  • Heckman, Jonathan J.; Morrison, David R.; Vafa, Cumrun
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/JHEP05(2014)028

6D SCFTs and gravity
journal, June 2015

  • Del Zotto, Michele; Heckman, Jonathan J.; Morrison, David R.
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)158

Breaking GUT groups in F-theory
journal, January 2011


Computing brane and flux superpotentials in F-theory compactifications
journal, April 2010

  • Grimm, Thomas W.; Ha, Tae-Won; Klemm, Albrecht
  • Journal of High Energy Physics, Vol. 2010, Issue 4
  • DOI: 10.1007/JHEP04(2010)015

The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications
journal, January 2015


Statistics of F-theory flux vacua for particle physics
journal, November 2015


Lattice points in high-dimensional spheres
journal, March 1990

  • Mazo, J. E.; Odlyzko, A. M.
  • Monatshefte für Mathematik, Vol. 110, Issue 1
  • DOI: 10.1007/BF01571276

On minimal models of elliptic threefolds
journal, March 1991


Complete classification of reflexive polyhedra in four dimensions
journal, January 2000

  • Kreuzer, Maximilian; Skarke, Harald
  • Advances in Theoretical and Mathematical Physics, Vol. 4, Issue 6
  • DOI: 10.4310/ATMP.2000.v4.n6.a2

hypersurfaces in algebraic tori
journal, February 1993


Calabi-Yau four-folds for M- and F-theory compactifications
journal, May 1998


Calabi-Yau 4-folds and toric fibrations
journal, July 1998


Geometric singularities and enhanced gauge symmetries
journal, December 1996


    Works referencing / citing this record:

    Computational complexity of vacua and near-vacua in field and string theory
    journal, February 2019


    Quadrillion F -Theory Compactifications with the Exact Chiral Spectrum of the Standard Model
    journal, September 2019


    Emergence of Weak Coupling at Large Distance in Quantum Gravity
    journal, August 2018


    Towards string theory expectations for photon couplings to axionlike particles
    journal, November 2019


    String theory and the dark glueball problem
    journal, February 2017


    The String Theory Landscape
    journal, July 2019


    Algorithmic universality in F-theory compactifications
    journal, December 2017


    Lightest Visible-Sector Supersymmetric Particle is Likely to be Unstable
    journal, October 2016


    Landscape solution to the SUSY flavor and C P problems
    journal, December 2019


    Swampland conjectures and late-time cosmology
    journal, April 2019