Global half-BPS $AdS_2\times S^6$ solutions in Type IIB

We investigate half-BPS Type IIB supergravity solutions with spacetime geometry $AdS_2\times S^6$ warped over a Riemann surface $\Sigma$. The general local solution was obtained in earlier work in terms of two holomorphic functions $\mathcal A_\pm$ on $\Sigma$. In the first part of this paper we seek global solutions corresponding to the near-horizon behavior of $(p,q)$-string junctions. We identify the type of singularity in $\mathcal A_\pm$ needed at the boundary of $\Sigma$ to match the solutions locally onto the classic $(p,q)$-string solution. We construct solutions with multiple $(p,q)$-strings, but the existence of geodesically complete solutions remains unsettled. In a second part we construct multi-parameter families of non-compact globally regular and geodesically complete solutions with asymptotic regions and an $AdS_2$ throat which caps off smoothly.