Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors

Understand

We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for four-dimensional F-theory compactifications on elliptic Calabi-Yau fourfolds with rank two Mordell-Weil group.

• The general elliptic fiber is the Calabi-Yau onefold in dP_2.
• We classify its resolved elliptic fibrations over a general base B.
• The study of singularities of these fibrations leads to explicit matter representations, that we determine both for U(1)xU(1) and SU(5)xU(1)xU(1) constructions.