Towards the Standard Model in F-theory

Understand

This article explores possible embeddings of the Standard Model gauge group and its matter representations into F-theory.

• To this end we construct elliptic fibrations with gauge group SU(3)xSU(2)xU(1)xU(1) as suitable restrictions of a ${\rm Bl}_2{\mathbb P}^2$-fibration with rank-two Mordell-Weil group.
• We analyse the five inequivalent toric enhancements to gauge group SU(3)xSU(2) along two independent divisors W_3 and W_2 in the base.
• For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental (3,2), three types of (1,2) representations and five types of (3,1) representations (plus conjugates), in addition to charged singlet states.