Upper bound on the Atiyah-Singer index from tadpole cancellation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911768581767168 |
|---|---|
| author | Ishiguro, Keiya Kai, Takafumi Nishimura, Satsuki Otsuka, Hajime Takeuchi, Maki |
| author_facet | Ishiguro, Keiya Kai, Takafumi Nishimura, Satsuki Otsuka, Hajime Takeuchi, Maki |
| contents | We propose an upper bound on the Atiyah-Singer index in the effective action of string theory. For $E_8 \times E_8^\prime$ and $SO(32)$ heterotic string theories on smooth Calabi-Yau threefolds with line bundles, we find that the tadpole cancellation and supersymmetry conditions lead to an upper bound on the generation number of quarks and leptons as well as Higgs doublets. By taking into account the observed value of four-dimensional gauge couplings and the supergravity approximation, we explicitly evaluate the bound on favorable complete intersection Calabi-Yau threefolds. The bound can be extended to Calabi-Yau threefolds in the Kreuzer-Skarke database. We also put the upper bound on the Atiyah-Singer index in Type IIB/F-theory compactifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12421 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Upper bound on the Atiyah-Singer index from tadpole cancellation Ishiguro, Keiya Kai, Takafumi Nishimura, Satsuki Otsuka, Hajime Takeuchi, Maki High Energy Physics - Theory High Energy Physics - Phenomenology We propose an upper bound on the Atiyah-Singer index in the effective action of string theory. For $E_8 \times E_8^\prime$ and $SO(32)$ heterotic string theories on smooth Calabi-Yau threefolds with line bundles, we find that the tadpole cancellation and supersymmetry conditions lead to an upper bound on the generation number of quarks and leptons as well as Higgs doublets. By taking into account the observed value of four-dimensional gauge couplings and the supergravity approximation, we explicitly evaluate the bound on favorable complete intersection Calabi-Yau threefolds. The bound can be extended to Calabi-Yau threefolds in the Kreuzer-Skarke database. We also put the upper bound on the Atiyah-Singer index in Type IIB/F-theory compactifications. |
| title | Upper bound on the Atiyah-Singer index from tadpole cancellation |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2308.12421 |