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

Understand

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.