One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
- Cvetič, Mirjam et al
- arXiv:2203.03644CERN-TH-2022-032LMU-ASC 10/22UPR-1316-T
 | Strings and 5-branes, which are represented as lines in the perpendicular plane, form junctions, where the $\colpq{p}{q}$-charge at each vertex is conserved (left). In the presence of 7-branes, they undergo monodromy transformations \eqref{eq:monodromy_on_prongs} when they cross a branch cut (middle). By a Hanany--Witten transition, the same junction can be represented as having a prong on the 7-brane (right). |
 | A loop junction $\boldsymbol\ell_{(r,s)}$ around a collection of 7-branes with overall monodromy $M$. The asymptotic charge $\colpq{p}{q} = \colpq{r'}{s'} - \colpq{r}{s} = (M - \mathbb{1}) \colpq{r}{s}$ is in general non-zero. |
 | The self-pairing of a 3-pronged junction (left) can be separated into contributions from the ends on 7-branes and the vertex, see \eqref{eq:self_pairing_3-pronged}. When there are no prongs ending on 7-branes, such as for loop juncions (right), the only contribution is that of the vertex. |
 | Construction of extended weight junctions. Since the $\colpq{r}{s}$-charges that appear in the loop are in general fractional, the prongs ending on the 7-branes after pulling the loop across also have fractional coefficients. |
 | Root junctions of $\mathfrak{sp}$ algebra (the double arrow denotes the factor of 2 required by evenness on O7$^+$). |
 | String junction lattice for rank $(2,18)$ theories. |
 | String junction lattice for rank $(2,10)$ theories. |
 | String junction lattice for rank $(2,2)$ theories. |