Learning non-Higgsable gauge groups in 4D F-theory

Wang, Yi-Nan; Zhang, Zhibai

doi:10.1007/jhep08(2018)009

Title: Learning non-Higgsable gauge groups in 4D F-theory

Abstract

We apply machine learning techniques to solve a specific classification problem in 4D F-theory. For a divisor D on a given complex threefold base, we want to read out the non-Higgsable gauge group on it using local geometric information near D. The input features are the triple intersection numbers among divisors near D and the output label is the non-Higgsable gauge group. We use decision tree to solve this problem and achieved 85%-98% out-of-sample accuracies for different classes of divisors, where the data sets are generated from toric threefold bases without (4,6) curves. We have explicitly generated a large number of analytic rules directly from the decision tree and proved a small number of them. As a crosscheck, we applied these decision trees on bases with (4,6) curves as well and achieved high accuracies. Additionally, we have trained a decision tree to distinguish toric (4,6) curves as well. Finally, we present an application of these analytic rules to construct local base configurations with interesting gauge groups such as SU(3).

Authors:

Wang, Yi-Nan ^[1]; Zhang, Zhibai ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics, Dept. of Physics
New York Univ. (NYU), NY (United States). Tandon School of Engineering, Dept. of Finance and Risk Engineering

Publication Date:: Fri Aug 03 00:00:00 EDT 2018

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

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1505580

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: 2018; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Differential and Algebraic Geometry; F-Theory

Citation Formats


                    Wang, Yi-Nan, and Zhang, Zhibai. Learning non-Higgsable gauge groups in 4D F-theory.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep08(2018)009.

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                    Wang, Yi-Nan, & Zhang, Zhibai. Learning non-Higgsable gauge groups in 4D F-theory.  United States.  https://doi.org/10.1007/jhep08(2018)009

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                    Wang, Yi-Nan, and Zhang, Zhibai. Fri .  
"Learning non-Higgsable gauge groups in 4D F-theory".  United States.  https://doi.org/10.1007/jhep08(2018)009.  https://www.osti.gov/servlets/purl/1505580.

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@article{osti_1505580,

  title        = {Learning non-Higgsable gauge groups in 4D F-theory},

  author       = {Wang, Yi-Nan and Zhang, Zhibai},

  abstractNote = {We apply machine learning techniques to solve a specific classification problem in 4D F-theory. For a divisor D on a given complex threefold base, we want to read out the non-Higgsable gauge group on it using local geometric information near D. The input features are the triple intersection numbers among divisors near D and the output label is the non-Higgsable gauge group. We use decision tree to solve this problem and achieved 85%-98% out-of-sample accuracies for different classes of divisors, where the data sets are generated from toric threefold bases without (4,6) curves. We have explicitly generated a large number of analytic rules directly from the decision tree and proved a small number of them. As a crosscheck, we applied these decision trees on bases with (4,6) curves as well and achieved high accuracies. Additionally, we have trained a decision tree to distinguish toric (4,6) curves as well. Finally, we present an application of these analytic rules to construct local base configurations with interesting gauge groups such as SU(3).},

  doi          = {10.1007/jhep08(2018)009},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 8,

  volume       = 2018,

  place        = {United States},

  year         = {Fri Aug 03 00:00:00 EDT 2018},

  month        = {Fri Aug 03 00:00:00 EDT 2018}

}

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Searching the landscape of flux vacua with genetic algorithms
text, January 2019

Cole, A.; Schachner, Andreas; Shiu, G.
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DOI: 10.17863/cam.79204

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Title: Learning non-Higgsable gauge groups in 4D F-theory

Abstract

Citation Formats

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

Introduction to Toric Varieties. (AM-131) book, December 1993

A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua journal, January 2016

On E 8 and F-theory GUTs journal, June 2015

Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds: Enhanced gauge symmetry in 6D F-theory models… journal, August 2016

Matter and singularities journal, January 2012

The Geometry of Toric Varieties journal, April 1978

Terminal singularities, Milnor numbers, and matter in F-theory journal, January 2018

Tate’s algorithm and F-theory journal, August 2011

Matter from geometry journal, July 1997

Machine learning in the string landscape journal, September 2017

Distribution of the number of generations in flux compactifications journal, December 2014

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

Scanning the skeleton of the 4D F-theory landscape journal, January 2018

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

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

Non-toric bases for elliptic Calabi–Yau threefolds and 6D F-theory vacua journal, January 2017

Geometric singularities and enhanced gauge symmetries journal, December 1996

Classifying bases for 6D F-theory models journal, January 2012

Machine learning of Calabi-Yau volumes journal, September 2017

Tuned and non-Higgsable U(1)s in F-theory journal, March 2017

Algorithmic universality in F-theory compactifications journal, December 2017

Machine-learning the string landscape journal, November 2017

Codimension-three bundle singularities in F-theory journal, June 2002

Lectures on F-theory compactifications and model building journal, October 2010

Anomalies and the Euler characteristic of elliptic Calabi–Yau threefolds journal, January 2012

Evidence for F-theory journal, June 1996

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

Flux compactification journal, May 2007

Evolving neural networks with genetic algorithms to study the string landscape journal, August 2017

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

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

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

Lectures on Constructing String Vacua book, January 2008

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

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

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

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

6d Conformal matter journal, February 2015

Type IIA Moduli Stabilization text, January 2005

Searching the landscape of flux vacua with genetic algorithms text, January 2019

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

Introduction to Toric Varieties. (AM-131)
book, December 1993

A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
journal, January 2016

On E 8 and F-theory GUTs
journal, June 2015

Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds: Enhanced gauge symmetry in 6D F-theory models…
journal, August 2016

Matter and singularities
journal, January 2012

The Geometry of Toric Varieties
journal, April 1978

Terminal singularities, Milnor numbers, and matter in F-theory
journal, January 2018

Tate’s algorithm and F-theory
journal, August 2011

Matter from geometry
journal, July 1997

Machine learning in the string landscape
journal, September 2017

Distribution of the number of generations in flux compactifications
journal, December 2014

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

Scanning the skeleton of the 4D F-theory landscape
journal, January 2018

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

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

Non-toric bases for elliptic Calabi–Yau threefolds and 6D F-theory vacua
journal, January 2017

Geometric singularities and enhanced gauge symmetries
journal, December 1996

Classifying bases for 6D F-theory models
journal, January 2012

Machine learning of Calabi-Yau volumes
journal, September 2017

Tuned and non-Higgsable U(1)s in F-theory
journal, March 2017

Algorithmic universality in F-theory compactifications
journal, December 2017

Machine-learning the string landscape
journal, November 2017

Codimension-three bundle singularities in F-theory
journal, June 2002

Lectures on F-theory compactifications and model building
journal, October 2010

Anomalies and the Euler characteristic of elliptic Calabi–Yau threefolds
journal, January 2012

Evidence for F-theory
journal, June 1996

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

Flux compactification
journal, May 2007

Evolving neural networks with genetic algorithms to study the string landscape
journal, August 2017

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

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

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

Lectures on Constructing String Vacua
book, January 2008

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

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

Non-Higgsable clusters for 4D F-theory models
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On the classification of 6D SCFTs and generalized ADE orbifolds
journal, May 2014

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Type IIA Moduli Stabilization
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