Weyl symmetry in $(D_4,D_4)$ conformal matter on a circle

TL;DR

This paper investigates Weyl symmetry in 5-brane web constructions of $(D_4,D_4)$ conformal matter theories on a circle, revealing affine $E_8$ symmetry and multiple invariant Coulomb branch parameter sets.

Contribution

It demonstrates that these theories possess affine $E_8$ Weyl symmetry in their brane web representations, a novel insight into their global symmetry structure.

Findings

Affine $E_8$ Weyl symmetry in all studied theories

Existence of 64 invariant Coulomb branch parameter sets for $N extgreater=2$

Identification of symmetry enhancement in brane web configurations

Abstract

We study Weyl symmetry in quadrivalently glued 5-brane webs of rank $N$ $(D_4,D_4)$ conformal matter theories on a circle. We find that these theories all have affine $E_8$ Weyl symmetry in their brane webs, which indicates that they all have affine $E_8$ global symmetry. When $N\geq 2$, the theory has 64 different sets of affine $E_8$ invariant Coulomb branch parameters.