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

• Published in: Physics letters. B Vol. 803; p. 135333
• Main Authors: Fukuchi, Shin, Kan, Naoto, Kuramochi, Rinto, Mizoguchi, Shun'ya, Tashiro, Hitomi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 10-04-2020; Elsevier
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2020.135333

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 P1 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 I0⁎ 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.