Physical Yukawa Couplings in Heterotic String Compactifications
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| Format: | Preprint |
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2024
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| author | Butbaia, Giorgi Peña, Damián Mayorga Tan, Justin Berglund, Per Hübsch, Tristan Jejjala, Vishnu Mishra, Challenger |
| author_facet | Butbaia, Giorgi Peña, Damián Mayorga Tan, Justin Berglund, Per Hübsch, Tristan Jejjala, Vishnu Mishra, Challenger |
| contents | One of the challenges of heterotic compactification on a Calabi-Yau threefold is to determine the physical $(\mathbf{27})^3$ Yukawa couplings of the resulting four-dimensional $\mathcal{N}=1$ theory. In general, the calculation necessitates knowledge of the Ricci-flat metric. However, in the standard embedding, which references the tangent bundle, we can compute normalized Yukawa couplings from the Weil-Petersson metric on the moduli space of complex structure deformations of the Calabi-Yau manifold. In various examples (the Fermat quintic, the intersection of two cubics in $\mathbb{P}^5$, and the Tian-Yau manifold), we calculate the normalized Yukawa couplings for $(2,1)$-forms using the Weil-Petersson metric obtained from the Kodaira-Spencer map. In cases where $h^{1,1}=1$, this is compared to a complementary calculation based on performing period integrals. A third expression for the normalized Yukawa couplings is obtained from a machine learned approximate Ricci-flat metric making use of explicit harmonic representatives. The excellent agreement between the different approaches opens the door to precision string phenomenology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Physical Yukawa Couplings in Heterotic String Compactifications Butbaia, Giorgi Peña, Damián Mayorga Tan, Justin Berglund, Per Hübsch, Tristan Jejjala, Vishnu Mishra, Challenger High Energy Physics - Theory High Energy Physics - Phenomenology One of the challenges of heterotic compactification on a Calabi-Yau threefold is to determine the physical $(\mathbf{27})^3$ Yukawa couplings of the resulting four-dimensional $\mathcal{N}=1$ theory. In general, the calculation necessitates knowledge of the Ricci-flat metric. However, in the standard embedding, which references the tangent bundle, we can compute normalized Yukawa couplings from the Weil-Petersson metric on the moduli space of complex structure deformations of the Calabi-Yau manifold. In various examples (the Fermat quintic, the intersection of two cubics in $\mathbb{P}^5$, and the Tian-Yau manifold), we calculate the normalized Yukawa couplings for $(2,1)$-forms using the Weil-Petersson metric obtained from the Kodaira-Spencer map. In cases where $h^{1,1}=1$, this is compared to a complementary calculation based on performing period integrals. A third expression for the normalized Yukawa couplings is obtained from a machine learned approximate Ricci-flat metric making use of explicit harmonic representatives. The excellent agreement between the different approaches opens the door to precision string phenomenology. |
| title | Physical Yukawa Couplings in Heterotic String Compactifications |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2401.15078 |