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Recent advances in F‐theory compactifications
Author(s) -
Weigand T.
Publication year - 2012
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.201200032
Subject(s) - f theory , holomorphic function , codimension , pure mathematics , physics , theoretical physics , fibered knot , gravitational singularity , intersection theory , brane cosmology , abelian group , gauge theory , intersection (aeronautics) , holonomy , yukawa potential , mathematics , string theory , mathematical physics , particle physics , quantum mechanics , differential algebraic equation , ordinary differential equation , aerospace engineering , engineering , differential equation
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 G 4 ‐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.