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Box Graphs and Singular Fibers
"... drm physics.ucsb.edu We determine the higher codimension fibers of elliptically fibered CalabiYau fourfolds with section by studying the threedimensional N = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of Mtheory compactified on the associated Weierst ..."
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drm physics.ucsb.edu We determine the higher codimension fibers of elliptically fibered CalabiYau fourfolds with section by studying the threedimensional N = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of Mtheory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping ” of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic CalabiYau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, nonKodaira, fiber types for E6, E7 and E8. ar X iv
Non abelian gauge symmetry and the Higgs mechanism in Ftheory. arXiv:1402.5962
"... Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in Ftheory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even nonabelian gauge theories have not been fully understood in global Ftheory compactifications. We prese ..."
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Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in Ftheory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even nonabelian gauge theories have not been fully understood in global Ftheory compactifications. We present a systematic discussion of using singularity deformation, which does describe the spontaneous breaking of gauge symmetry in Ftheory, to study nonabelian gauge symmetry. Since this branch of the moduli space also exists in the defining Mtheory compactification, it provides the only known description of gauge theory states which exists in both pictures; they are string junctions in Ftheory. Utilizing deformations, we study a number of new examples, including nonperturbative descriptions of SU(3) and SU(2) gauge theories on sevenbranes which do not admit a weakly coupled type IIb description. It may be of phenomenological interest that these nonperturbative descriptions do not exist for higher rank SU(N) theories. ar
J H E P08(2014)025
, 2014
"... Geometric constraints in dual Ftheory and heterotic string compactifications ..."
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Geometric constraints in dual Ftheory and heterotic string compactifications