A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

Taylor, Washington; Wang, Yi-Nan

doi:10.1007/JHEP01(2016)137

Title: A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

Journal Article · Fri Jan 22 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP01(2016)137· OSTI ID:1327305

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

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

Here, we use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be ~ 10⁴⁸. Moreover, the distribution of bases peaks around h^1,1 ~ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We also find that the number of non-Higgsable gauge group factors grows roughly linearly in h^1,1 of the threefold base. Typical bases have ~ 6 isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3) x SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) x SU(2) is the third most common connected two-factor product group, following SU(2) x SU(2) and G2 x SU(2), which arise more frequently.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0012567

OSTI ID:: 1327305

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 1; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 38 works

Citation information provided by
Web of Science

References (56)

Evidence for F-theory Vafa, Cumrun Nuclear Physics B, Vol. 469, Issue 3 https://doi.org/10.1016/0550-3213(96)00172-1	journal	June 1996
Compactifications of F-theory on Calabi-Yau threefolds. (I) Morrison, David R.; Vafa, Cumrun Nuclear Physics B, Vol. 473, Issue 1-2 https://doi.org/10.1016/0550-3213(96)00242-8	journal	August 1996
Compactifications of F-theory on Calabi-Yau threefolds (II) Morrison, David R.; Vafa, Cumrun Nuclear Physics B, Vol. 476, Issue 3 https://doi.org/10.1016/0550-3213(96)00369-0	journal	September 1996
Global aspects of the space of 6D $ \mathcal{N} = 1 $ supergravities Kumar, Vijay; Morrison, David R.; Taylor, Washington Journal of High Energy Physics, Vol. 2010, Issue 11 https://doi.org/10.1007/JHEP11(2010)118	journal	November 2010
Toric bases for 6D F-theory models Morrison, D. R.; Taylor, W. Fortschritte der Physik, Vol. 60, Issue 11-12 https://doi.org/10.1002/prop.201200086	journal	May 2012
On the Hodge structure of elliptically fibered Calabi-Yau threefolds Taylor, Washington Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)032	journal	August 2012
6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces Martini, Gabriella; Taylor, Washington Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)061	journal	June 2015
Calabi-Yau threefolds with large h 2,1 Johnson, Samuel B.; Taylor, Washington Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)023	journal	October 2014
Geometric constraints in dual F-theory and heterotic string compactifications Anderson, Lara B.; Taylor, Washington Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)025	journal	August 2014
Non-Higgsable QCD and the standard model spectrum in F-theory Grassi, Antonella; Halverson, James; Shaneson, Julius Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)086	journal	January 2015
Non-Higgsable clusters for 4D F-theory models Morrison, David R.; Taylor, Washington Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)080	journal	May 2015
ℙ 1 $$ {\mathrm{\mathbb{P}}}^1 $$ -bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models Halverson, James; Taylor, Washington Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)086	journal	September 2015
Calabi-Yau four-folds for M- and F-theory compactifications Klemm, A.; Lian, B.; Roan, S. -S Nuclear Physics B, Vol. 518, Issue 3 https://doi.org/10.1016/S0550-3213(97)00798-0	journal	May 1998
Heterotic string/F-theory duality from mirror symmetry Berglund, P.; Mayr, P. Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 6 https://doi.org/10.4310/ATMP.1998.v2.n6.a4	journal	January 1998
Structure in 6D and 4D $ \mathcal{N}=1 $ supergravity theories from F-theory Grimm, Thomas W.; Taylor, Washington Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)105	journal	October 2012
On Compact Analytic Surfaces: II Kodaira, K. The Annals of Mathematics, Vol. 77, Issue 3 https://doi.org/10.2307/1970131	journal	May 1963
Geometric singularities and enhanced gauge symmetries Bershadsky, M.; Intriligator, K.; Kachru, S. Nuclear Physics B, Vol. 481, Issue 1-2 https://doi.org/10.1016/S0550-3213(96)90131-5	journal	December 1996
Tate’s algorithm and F-theory Katz, Sheldon; Morrison, David R.; Schäfer-Nameki, Sakura Journal of High Energy Physics, Vol. 2011, Issue 8 https://doi.org/10.1007/JHEP08(2011)094	journal	August 2011
Anomalies and the Euler characteristic of elliptic Calabi–Yau threefolds Grassi, Antonella; Morrison, David R. Communications in Number Theory and Physics, Vol. 6, Issue 1 https://doi.org/10.4310/CNTP.2012.v6.n1.a2	journal	January 2012
Introduction to Toric Varieties. (AM-131) Fulton, William Annals of Mathematics Studies series, Vol. 131 https://doi.org/10.1515/9781400882526	book	December 1993
On minimal models of elliptic threefolds Grassi, Antonella Mathematische Annalen, Vol. 290, Issue 1 https://doi.org/10.1007/BF01459246	journal	March 1991
Comments on string dynamics in six dimensions Seiberg, N.; Witten, E. Nuclear Physics B, Vol. 471, Issue 1-2 https://doi.org/10.1016/0550-3213(96)00189-7	journal	July 1996
Non-trivial fixed points of the renormalization group in six dimensions Seiberg, Nathan Physics Letters B, Vol. 390, Issue 1-4 https://doi.org/10.1016/S0370-2693(96)01424-4	journal	January 1997
On the classification of 6D SCFTs and generalized ADE orbifolds Heckman, Jonathan J.; Morrison, David R.; Vafa, Cumrun Journal of High Energy Physics, Vol. 2014, Issue 5 https://doi.org/10.1007/JHEP05(2014)028	journal	May 2014
6D SCFTs and gravity Del Zotto, Michele; Heckman, Jonathan J.; Morrison, David R. Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)158	journal	June 2015
Introduction to the Mori Program Matsuki, Kenji Universitext https://doi.org/10.1007/978-1-4757-5602-9	book	January 2002
Codimension-three bundle singularities in F-theory Candelas, Philip; Diaconescu, Duiliu-Emanuel; Florea, Bogdan Journal of High Energy Physics, Vol. 2002, Issue 06 https://doi.org/10.1088/1126-6708/2002/06/014	journal	June 2002
Arithmetic on elliptic threefolds Wazir, Rania Compositio Mathematica, Vol. 140, Issue 03 https://doi.org/10.1112/S0010437X03000381	journal	May 2004
Landau-Ginzburg vacua of string, M- and F-theory at c=12 Lynker, Monika; Schimmrigk, Rolf; Wißkirchen, Andreas Nuclear Physics B, Vol. 550, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00204-7	journal	June 1999
Weight Systems for Toric Calabi-Yau Varieties and Reflexivity of Newton Polyhedra Skarke, Harald Modern Physics Letters A, Vol. 11, Issue 20 https://doi.org/10.1142/S0217732396001636	journal	June 1996
Searching for K3 fibrations Avram, A. C.; Kreuzer, M.; Mandelberg, M. Nuclear Physics B, Vol. 494, Issue 3 https://doi.org/10.1016/S0550-3213(97)00214-9	journal	June 1997
Complete classification of reflexive polyhedra in four dimensions Kreuzer, Maximilian; Skarke, Harald Advances in Theoretical and Mathematical Physics, Vol. 4, Issue 6 https://doi.org/10.4310/ATMP.2000.v4.n6.a2	journal	January 2000
An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts Candelas, Philip; Constantin, Andrei; Skarke, Harald Communications in Mathematical Physics, Vol. 324, Issue 3 https://doi.org/10.1007/s00220-013-1802-2	journal	October 2013
Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds Gray, James; Haupt, Alexander S.; Lukas, Andre Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)093	journal	September 2014
Model building with $F$-theory Donagi, Ron; Wijnholt, Martijn Advances in Theoretical and Mathematical Physics, Vol. 15, Issue 5 https://doi.org/10.4310/ATMP.2011.v15.n5.a2	journal	January 2011
GUTs and exceptional branes in F-theory — I Beasley, Chris; Heckman, Jonathan J.; Vafa, Cumrun Journal of High Energy Physics, Vol. 2009, Issue 01 https://doi.org/10.1088/1126-6708/2009/01/058	journal	January 2009
GUTs and exceptional branes in F-theory — II. Experimental predictions Beasley, Chris; Heckman, Jonathan J.; Vafa, Cumrun Journal of High Energy Physics, Vol. 2009, Issue 01 https://doi.org/10.1088/1126-6708/2009/01/059	journal	January 2009
The <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> effective action of F-theory compactifications Grimm, Thomas W. Nuclear Physics B, Vol. 845, Issue 1 https://doi.org/10.1016/j.nuclphysb.2010.11.018	journal	April 2011
F-theory fluxes, chirality and Chern-Simons theories Grimm, Thomas W.; Hayashi, Hirotaka Journal of High Energy Physics, Vol. 2012, Issue 3 https://doi.org/10.1007/JHEP03(2012)027	journal	March 2012
Matter from geometry Katz, Sheldon; Vafa, Cumrun Nuclear Physics B, Vol. 497, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)00280-0	journal	July 1997
Matter and singularities Morrison, David R.; Taylor, Washington Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)022	journal	January 2012
Small resolutions of SU(5)-models in F-theory Esole, Mboyo; Yau, Shing-Tung Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 6 https://doi.org/10.4310/ATMP.2013.v17.n6.a1	journal	January 2013
The Tate form on steroids: resolution and higher codimension fibers Lawrie, Craig; Schäfer-Nameki, Sakura Journal of High Energy Physics, Vol. 2013, Issue 4 https://doi.org/10.1007/JHEP04(2013)061	journal	April 2013
Phases, flops and F-theory: SU(5) gauge theories Hayashi, Hirotaka; Lawrie, Craig; Schäfer-Nameki, Sakura Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)046	journal	October 2013
Box graphs and singular fibers Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R. Journal of High Energy Physics, Vol. 2014, Issue 5 https://doi.org/10.1007/JHEP05(2014)048	journal	May 2014
Stable singularities in string theory Aspinwall, Paul S.; Morrison, David R.; Gross, Mark Communications in Mathematical Physics, Vol. 178, Issue 1 https://doi.org/10.1007/BF02104911	journal	May 1996
F-theory on genus-one fibrations Braun, Volker; Morrison, David R. Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)132	journal	August 2014
Physics of F-theory compactifications without section Anderson, Lara B.; García-Etxebarria, Iñaki; Grimm, Thomas W. Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)156	journal	December 2014
Discrete gauge symmetries by Higgsing in four-dimensional F-theory compactifications Mayrhofer, Christoph; Palti, Eran; Till, Oskar Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)068	journal	December 2014
F-theory on all toric hypersurface fibrations and its Higgs branches Klevers, Denis; Mayorga Peña, Damián Kaloni; Oehlmann, Paul-Konstantin Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)142	journal	January 2015
F-theory vacua with $Z_{3}$ gauge symmetry Cvetič, Mirjam; Donagi, Ron; Klevers, Denis Nuclear Physics B, Vol. 898 https://doi.org/10.1016/j.nuclphysb.2015.07.011	journal	September 2015
A finiteness theorem for elliptic Calabi-Yau threefolds Gross, Mark Duke Mathematical Journal, Vol. 74, Issue 2 https://doi.org/10.1215/S0012-7094-94-07414-0	journal	May 1994
Counting Flux Vacua Ashok, Sujay K.; Douglas, Michael R. Journal of High Energy Physics, Vol. 2004, Issue 01 https://doi.org/10.1088/1126-6708/2004/01/060	journal	January 2004
Distributions of flux vacua Denef, Frederik; Douglas, Michael R. Journal of High Energy Physics, Vol. 2004, Issue 05 https://doi.org/10.1088/1126-6708/2004/05/072	journal	May 2004
The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications Braun, A. P.; Watari, T. Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)047	journal	January 2015
Flux compactification Douglas, Michael R.; Kachru, Shamit Reviews of Modern Physics, Vol. 79, Issue 2 https://doi.org/10.1103/RevModPhys.79.733	journal	May 2007

Cited By (6)

Hidden sectors in string theory: kinetic mixings, fifth forces and quintessence Acharya, Bobby Samir; Maharana, Anshuman; Muia, Francesco Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/jhep03(2019)048	journal	March 2019
String theory and the dark glueball problem Halverson, James; Nelson, Brent D.; Ruehle, Fabian Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-01481	text	January 2017
String Theory and the Dark Glueball Problem Halverson, James; Nelson, Brent D.; Ruehle, Fabian arXiv https://doi.org/10.48550/arxiv.1609.02151	text	January 2016
On Algorithmic Universality in F-theory Compactifications Halverson, James; Long, Cody; Sung, Benjamin arXiv https://doi.org/10.48550/arxiv.1706.02299	text	January 2017
On the Scarcity of Weak Coupling in the String Landscape Halverson, James; Long, Cody; Sung, Benjamin arXiv https://doi.org/10.48550/arxiv.1710.09374	text	January 2017
Scanning the skeleton of the 4D F-theory landscape Taylor, Washington; Wang, Yi-Nan arXiv https://doi.org/10.48550/arxiv.1710.11235	text	January 2017

Similar Records

The F-theory geometry with most flux vacua

Journal Article · Mon Dec 28 00:00:00 EST 2015 · Journal of High Energy Physics (Online) · OSTI ID:1327305

Taylor, Washington; Wang, Yi -Nan

Scanning the skeleton of the 4D F-theory landscape

Journal Article · Tue Jan 23 00:00:00 EST 2018 · Journal of High Energy Physics (Online) · OSTI ID:1327305

Taylor, Washington; Wang, Yi-Nan

Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers

Journal Article · Thu Feb 14 00:00:00 EST 2019 · Journal of High Energy Physics (Online) · OSTI ID:1327305

Huang, Yu-Chien; Taylor, Washington

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
97 MATHEMATICS AND COMPUTING
F-theory
superstring
vacua

Title: A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

Citation Formats

References (56)

Cited By (6)

Similar Records

Related Subjects