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

String and 5-brane junctions are shown to succinctly classify all known 8D <math display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> string vacua. This requires an extension of the description for ordinary <math display="inline"><mo stretchy="false">[</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo stretchy="false">]</mo></math>-7-branes to consistently include <math display="inline"><mrow><mi mathvariant="normal">O</mi><msup><mrow><mn>7</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> planes, which then naturally encodes the dynamics of <math display="inline"><msub><mi mathvariant="fraktur">sp</mi><mi>n</mi></msub></math> gauge algebras, including their <math display="inline"><mi>p</mi></math>-form center symmetries. Central to this analysis are loop junctions, i.e., strings/5-branes which encircle stacks of 7-branes and <math display="inline"><mrow><mrow><mi mathvariant="normal">O</mi><msup><mrow><mn>7</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow><mi mathvariant="normal">s</mi></mrow></math>. 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.