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Matter from multiply enhanced singularities in F-theory
Shun'ya Mizoguchi, Taro Tani
We investigate the geometrical structure of multiply enhanced codimension-two singularities in the model of six-dimensional F-theory, where the rank of the singularity incr…
Non-split singularities and conifold transitions in F-theory
Rinto Kuramochi, Shun'ya Mizoguchi, Taro Tani
In F-theory, if a fiber type of an elliptic fibration involves a condition that requires an exceptional curve to split into two irreducible components, it is called ``split'' or ``…
Magic square and half-hypermultiplets in F-theory
Rinto Kuramochi, Shun'ya Mizoguchi, Taro Tani
In six-dimensional F-theory/heterotic string theory, half-hypermultiplets arise only when they correspond to particular quaternionic Kähler symmetric spaces, which are mostly assoc…
Half-hypermultiplets and incomplete/complete resolutions in F-theory
Naoto Kan, Shun'ya Mizoguchi, Taro Tani
We consider resolutions of codimension-two enhanced singularities from to and from to in six-dimensional F-theory, where a half-hypermultiplet arises for…
Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications
Shun'ya Mizoguchi, Taro Tani
The Mordell-Weil lattices (MW lattices) associated to rational elliptic surfaces are classified into 74 types. Among them, there are cases in which the MW lattice is none of the we…
Looijenga's weighted projective space, Tate's algorithm and Mordell-Weil Lattice in F-theory and heterotic string theory
Shun'ya Mizoguchi, Taro Tani
It is now well known that the moduli space of a vector bundle for heterotic string compactifications to four dimensions is parameterized by a set of sections of a weighted projecti…