Affine Lie Algebras, String Junctions and 7-Branes

TL;DR

This paper explores how affine ADE Lie algebras can be realized through string junctions on 7-branes in Type IIB string theory, revealing algebraic structures via string configurations and their charges.

Contribution

It demonstrates the realization of affine ADE Lie algebras as string junctions on 7-branes and relates algebraic features to string configurations and charges.

Findings

Affine algebra is signaled by the imaginary root junction 'delta'

Level k constrains asymptotic (p,q) charges of junctions

Junction intersection form reproduces affine inner product

Abstract

We consider the realization of affine ADE Lie algebras as string junctions on mutually non-local 7-branes in Type IIB string theory. The existence of the affine algebra is signaled by the presence of the imaginary root junction ``delta'', which is realized as a string encircling the 7-brane configuration. The level k of an affine representation partially constrains the asymptotic (p,q) charges of string junctions departing the configuration. The junction intersection form reproduces the full affine inner product, plus terms in the asymptotic charges.