Recent advances in F-theory compactifications

Abstract

We review recent progress in the construction of F-theory compactifications on elliptically fibered Calabi-Yau 4-folds. Of special importance is the resolution of the singularities in complex codimension one, two and three. These encode 7-branes along holomorphic divisors carrying non-abelian gauge groups, localised matter at the intersection of pairs of 7-branes and Yukawa interactions, respectively. Toric methods admit the explicit construction of a large class of resolved 4-folds. In particular the matter surfaces and interaction points can be analysed in great detail via resolution by blow-up. Engineering chiral matter spectra requires non-trivial gauge bundles described as certain types of G₄-fluxes. The recent construction of such fluxes paves the way for globally defined 3-generation models e.g. of SU(5) GUT type, possibly including extra U(1) factors.