Model Building with F-Theory

Abstract

Despite much recent progress in model building with D-branes, it has been problematic to find a completely convincing explanation of gauge coupling unification. We extend the class of models by considering F-theory compactifications, which may incorporate unification more naturally. We explain how to derive the charged chiral spectrum and Yukawa couplings in N=1 compactifications of F-theory with G-flux. In a class of models which admit perturbative heterotic duals, we show that the F-theory and heterotic computations match.

Figures (5)

• Figure 1: Multi-pronged strings in $B_3$ lift to curves in $Y_4$, allowing for matter and gauge groups which cannot be obtained from ordinary open strings.
• Figure 2: One can degenerate the $K3$ surface into two $DP_9$ surfaces glued along an elliptic curve, with non-abelian gauge symmetries localized at the crosses. In this limit one may compare with the $E_8\times E_8$ heterotic string.
• Figure 3: Part of the heterotic compactification data consists of an elliptically fibered Calabi-Yau, together with a set of points on each elliptic fibre describing the Wilson lines of the ten-dimensional gauge group.
• Figure 4: To every $dP_9$-surface we may associate an elliptic curve with a set of points on it by intersecting a fixed elliptic fiber of the $dP_9$ with the set of $-1$-curves. Conversely by taking an elliptic curve with a set of points and thickening the points to ${\bf P}^1$'s, we obtain a $dP_9$ surface.
• Figure :