E-string and model building on a typical F-theory geometry
In recent scans of 4D F-theory geometric models, it was shown that a dominant majority of the base geometries only support $SU(2)$, $G_2$, $F_4$ and $E_8$ gauge groups. It is hence an important question whether the particle physics standard model can be embedded in these geometries or not. In this paper, we construct a standard model-like 4D gauge theory on a stack of 7-branes with a single $E_8$ gauge group. The chiral spectrum of standard model is realized by conformal matter localized on a complex curve within the $E_8$ 7-branes. These 4D matter fields precisely originate from a 6D E-string theory compactified on a complex curve. The particle spectrum of the E-string theory is read off from the M2 brane wrapping modes on a resolved elliptic Calabi-Yau threefold with non-flat fiber. Finally, the $E_8$ gauge group is broken to $SU(3)\times SU(2)\times U(1)\times U(1)^4$ after a gauge flux is introduced on the stack of 7-branes. We are able to obtain the desired three generations of standard model matter fields from the branching rule of 4D matter fields in $\mathbf{3875}$ representation of $E_8$. The Higgs sector is realized as bulk fields from the stack of 7-branes, which is responsible for the Yukawa coupling with matter fields on the curve.
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Jiahua Tian (add twitter)
Yi-Nan Wang (edit)
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11/07/18 06:03PM
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hep_th: [1811.02837] Jiahua Tian, Yi-Nan Wang : E-string and model building on a typical F-theory geometry https://t.co/qnEp3W0KQ8
GeorgeShiber: E-String Theory, F-Theory, and Embedding the Standard-Model Gauge-Group into a Single E8 Gauge Group https://t.co/Pg5Vhw1Lzp Very deep and important set of results! https://t.co/hNmL4hiEz9
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