arXiv subjects

Shin Fukuchi

Publications and source records attributed to Shin Fukuchi.

3 recordsLinked to original sources

arXiv2019

More on a dessin on the base: Kodaira exceptional fibers and mutually (non-)local branes

A "dessin d'enfant" is a graph embedded on a two-dimensional oriented surface named by Grothendieck. Recently we have developed a new way to keep track of non-localness among 7-branes in F-theory on an elliptic fibration over $P^1$ by drawing a triangulated "dessin" on the base. To further demonstrate the usefulness of this method, we provide three examples of its use. We first consider a deformation of the $I_0^*$ Kodaira fiber. With a dessin, we can immediately find out which pairs of 7-branes are (non-)local and compute their monodromies. We next identify the paths of string(-junction)s on the dessin by solving the mass geodesic equation. By numerically computing their total masses, we find that the Hanany-Witten effect has not occurred in this example. Finally, we consider the orientifold limit in the spectral cover/Higgs bundle approach. We observe the characteristic configuration presenting the cluster sub-structure of an O-plane found previously.

hep-th↗

arXiv2018

A dessin on the base: a description of mutually non-local 7-branes without using branch cuts

We consider the special roles of the zero loci of the Weierstrass invariants $g_2(\tau(z))$, $g_3(\tau(z))$ in F-theory on an elliptic fibration over $P^1$ or a further fibration thereof. They are defined as the zero loci of the coefficient functions $f(z)$ and $g(z)$ of a Weierstrass equation. They are thought of as complex co-dimension one objects and correspond to the two kinds of critical points of a dessin d'enfant of Grothendieck. The $P^1$ base is divided into several cell regions bounded by some domain walls extending from these planes and D-branes, on which the imaginary part of the $J$-function vanishes. This amounts to drawing a dessin with a canonical triangulation. We show that the dessin provides a new way of keeping track of mutual non-localness among 7-branes without employing unphysical branch cuts or their base point. With the dessin we can see that weak- and strong-coupling regions coexist and are located across an $S$-wall from each other. We also present a simple method for computing a monodromy matrix for an arbitrary path by tracing the walls it goes through.

hep-th↗

arXiv2018

On an Algebraic Structure of Dimensionally Reduced Magical Supergravity Theories

We study an algebraic structure of magical supergravities in three dimensions. We show that if the commutation relations among the generators of the quasi-conformal group in the super-Ehlers decomposition are in a particular form, then one can always find a parameterization of the group element in terms of various 3d bosonic fields that reproduces the 3d reduced Lagrangian of the corresponding magical supergravity. This provides a unified treatment of all the magical supergravity theories in finding explicit relations between the 3d dimensionally reduced Lagrangians and particular coset nonlinear sigma models. We also verify that the commutation relations of $E_{6(+2)}$, the quasi-conformal group for $\mathbb{A}=\mathbb{C}$, indeed satisfy this property, allowing the algebraic interpretation of the structure constants and scalar field functions as was done in the $F_{4(+4)}$ magical supergravity.

hep-th↗