One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions

TL;DR

This paper demonstrates that string and 5-brane junctions can classify all known 8-dimensional N=1 string vacua, revealing new insights into gauge symmetries and their higher-form center symmetries through loop junctions.

Contribution

It extends the junction framework to include O7+ planes, enabling a unified classification of 8d string vacua and their connection to 9d limits with affine symmetries.

Findings

Classification of 8d vacua via junctions including O7+ planes

Identification of loop junctions signaling affine symmetries

Reproduction of all 9d vacua, including disconnected components

Abstract

String and 5-brane junctions are shown to succinctly classify all known 8d ${\cal N}$=1 string vacua. This requires an extension of the description for ordinary $[p,q]$-7-branes to consistently include O7$^+$-planes, which then naturally encodes the dynamics of $\mathfrak{sp}_n$ gauge algebras, including their higher-form center symmetries. Central to this analysis are loop junctions, i.e., strings/5-branes which encircle stacks of 7-branes and O7$^+$'s. Loop junctions further signal the appearance of affine symmetries of emergent 9d descriptions at the 8d moduli space's boundaries. Such limits reproduce all 9d string vacua, including the two disconnected rank (1,1) moduli components.