# 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:

- 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:

- 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.
```

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

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

```
@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 = {2018},

month = {8}

}

*Citation information provided by*

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