Open string - string junction transitions

Abstract

It is confirmed that geodesic string junctions are necessary to describe the gauge vectors of symmetry groups that arise in the context of IIB superstrings compactified in the presence of nonlocal 7-branes. By examining the moduli space of 7-brane backgrounds for which the dilaton and axion fields are constant, we are able to describe explicitly and geometrically how open string geodesics can fail to be smooth, and how geodesic string junctions then become the relevant BPS representatives of the gauge bosons. The mechanisms that guarantee the existence and uniqueness of the BPS representative of any gauge vector are also shown to generalize to the case where the dilaton and axion fields are not constant.

Figures (17)

• Figure 1: The branes can be characterized by either the monodromies or the discontinuity at their branch cuts. The matrices $M$ and $K$ both induce a group homomorphism $\pi_1(S_0)\to\hbox{SL}(2,{\sf Z\!\!Z})$.
• Figure 2: As the branch cut is crossed anticlockwise both $\tau$ and $({p\atop q})$ are transformed by $K$.
• Figure 3: The local $\hbox{SL}(2,{\sf Z\!\!Z})$-transformation induced by $K_j$ in the shaded area relocates the cut of the ${\bf j}$-brane and changes the ${\bf i}$-brane to an ${\bf i'}$-brane. In the standard presentation the right picture reads ${\bf i'j}$ as $C_j'$ is to the right of $C_i$ and thus we have ${\bf ji}\longrightarrow{\bf i'j}$.
• Figure 4: The effect of a local $\hbox{SL}(2,{\sf Z\!\!Z})$-transformation induced by $K_A$ in the light and by $K_A^2$ in the dark shaded area results in the relocation of both A-cuts and the change of the C-brane into a B-brane: AAC$\longrightarrow$BAA.
• Figure 5: Two-singularity resolution of so(8). (a) The groups of three branes are located at the real points $z_0$ and $z_1$. (b) The singularities are mapped to $0$ and $w_1$ while the whole $z$-plane is mapped to the non-shaded region of the $w$-plane.