The F-theory geometry with most flux vacua

Taylor, Washington; Wang, Yi -Nan

doi:10.1007/JHEP12(2015)164

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 M_max gives rise to O(10^272,000) 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 M_max arises from a generic elliptic fibration over a specific toric threefold base B_max, 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 M_max, 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 M_max.

Authors:

Taylor, Washington ^[1]; Wang, Yi -Nan ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Publication Date:: 2015-12-28

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

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                    Taylor, Washington, and Wang, Yi -Nan. The F-theory geometry with most flux vacua.  United States: N. p., 2015. 
Web.  doi:10.1007/JHEP12(2015)164.

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                    Taylor, Washington, & Wang, Yi -Nan. The F-theory geometry with most flux vacua.  United States.  https://doi.org/10.1007/JHEP12(2015)164

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                    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.

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@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}

}

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Title: The F-theory geometry with most flux vacua

Abstract

Citation Formats

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

Evidence for F-theory journal, June 1996

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

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

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

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

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

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

Lattice points in high-dimensional spheres journal, March 1990

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

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

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

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

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

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

The Geometry of Toric Varieties journal, April 1978

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

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

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

6D SCFTs and gravity journal, June 2015

Breaking GUT groups in F-theory journal, January 2011

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

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

On minimal models of elliptic threefolds journal, March 1991

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

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

The Statistics of String/M Theory Vacua conference, January 2012

6D SCFTs and gravity text, January 2015

GUTs and Exceptional Branes in F-theory - I text, January 2008

GUTs and Exceptional Branes in F-theory - II: Experimental Predictions text, January 2008

Breaking GUT Groups in F-Theory preprint, January 2008

Computing Brane and Flux Superpotentials in F-theory Compactifications text, January 2009

On the Hodge structure of elliptically fibered Calabi-Yau threefolds text, January 2012

On the Classification of 6D SCFTs and Generalized ADE Orbifolds text, January 2013

6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces preprint, January 2014

Non-Higgsable clusters for 4D F-theory models text, January 2014

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

Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant text, January 2000

The statistics of string/M theory vacua text, January 2003

Counting Flux Vacua text, January 2003

Evidence for F-Theory text, January 1996

Compactifications of F-Theory on Calabi--Yau Threefolds -- II text, January 1996

Calabi-Yau fourfolds for M- and F-Theory compactifications text, January 1997

Toric Geometry and Enhanced Gauge Symmetry of F-Theory/Heterotic Vacua text, January 1997

F-theory, SO(32) and Toric Geometry text, January 1997

Landau-Ginzburg Vacua of String, M- and F-Theory at c=12 text, January 1998

The String Theory Landscape journal, July 2019

The string theory landscape journal, January 2015

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String Theory and the Dark Glueball Problem text, January 2016

On Algorithmic Universality in F-theory Compactifications text, January 2017

Swampland Conjectures and Late-Time Cosmology text, January 2018

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

Evidence for F-theory
journal, June 1996

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

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

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

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

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

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

Lattice points in high-dimensional spheres
journal, March 1990

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

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

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

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

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

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

The Geometry of Toric Varieties
journal, April 1978

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

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

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

6D SCFTs and gravity
journal, June 2015

Breaking GUT groups in F-theory
journal, January 2011

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

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

On minimal models of elliptic threefolds
journal, March 1991

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

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

The Statistics of String/M Theory Vacua
conference, January 2012

6D SCFTs and gravity
text, January 2015

GUTs and Exceptional Branes in F-theory - I
text, January 2008

GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
text, January 2008

Breaking GUT Groups in F-Theory
preprint, January 2008

Computing Brane and Flux Superpotentials in F-theory Compactifications
text, January 2009

On the Hodge structure of elliptically fibered Calabi-Yau threefolds
text, January 2012

On the Classification of 6D SCFTs and Generalized ADE Orbifolds
text, January 2013

6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
preprint, January 2014

Non-Higgsable clusters for 4D F-theory models
text, January 2014

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

Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant
text, January 2000

The statistics of string/M theory vacua
text, January 2003

Counting Flux Vacua
text, January 2003

Evidence for F-Theory
text, January 1996

Compactifications of F-Theory on Calabi--Yau Threefolds -- II
text, January 1996

Calabi-Yau fourfolds for M- and F-Theory compactifications
text, January 1997

Toric Geometry and Enhanced Gauge Symmetry of F-Theory/Heterotic Vacua
text, January 1997

F-theory, SO(32) and Toric Geometry
text, January 1997

Landau-Ginzburg Vacua of String, M- and F-Theory at c=12
text, January 1998

The String Theory Landscape
journal, July 2019

The string theory landscape
journal, January 2015

String theory and the dark glueball problem
text, January 2017

String Theory and the Dark Glueball Problem
text, January 2016

On Algorithmic Universality in F-theory Compactifications
text, January 2017

Swampland Conjectures and Late-Time Cosmology
text, January 2018