Non-simply-laced Lie algebras via F theory strings

TL;DR

This paper explores how non-simply-laced Lie algebras emerge in F theory through string junctions, detailing specific foldings and their string representations, advancing understanding of symmetry enhancements in string theory.

Contribution

It provides an explicit string junction description of the foldings of certain Lie algebras, extending the geometric and algebraic understanding of symmetry enhancements in F theory.

Findings

Explicit description of D_{2n} to B_n folding via junctions

Description of E_6 to F_4 and D_4 to G_2 foldings using string junctions

Discussion of C_n case with partial insights

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.