Upper bound on the Atiyah-Singer index from tadpole cancellation

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Hauptverfasser: Ishiguro, Keiya, Kai, Takafumi, Nishimura, Satsuki, Otsuka, Hajime, Takeuchi, Maki
Format: Preprint
Veröffentlicht: 2023
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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