Non-simply-laced Lie algebras via F theory strings

Abstract

In order to describe the appearance in F theory of the non--simply--laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings. We also discuss the case of C_n, but we are unable in this case to provide a string interpretation.

arXiv comment24 pages, 3 figures

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• T-Branes, String Junctions, and 6D SCFTs
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• Tate Form and Weak Coupling Limits in F-theory
• F-theory Family Unification
• F-theory and the Witten Index
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
• F-theory Yukawa Couplings and Supersymmetric Quantum Mechanics
• Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra
• A dessin on the base: a description of mutually non-local 7-branes without using branch cuts