Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus

Regularity and topology conditions are imposed on the exact Type IIB solutions on $AdS_4 \times S^2 \times S^2 \times \Sigma $ with 16 supersymmetries, which were derived in a companion paper. We construct an infinite class of regular solutions with varying dilaton, and non-zero 3-form fluxes. Our solutions may be viewed as the fully back-reacted geometries of $AdS_5 \times S^5$ (or more generally, Janus) doped with D5 and/or NS5 branes. The solutions are parametrized by the choice of an arbitrary genus $g$ hyper-elliptic Riemann surface $\Sigma $ with boundary, all of whose branch points are restricted to lie on a line. For genus 0, the Janus solution with 16 supersymmetries and 6 real parameters is recovered; its topology coincides with that of $AdS_5 \times S^5$. The genus $g\geq 1$ solutions are parametrized by a total of $4g+6$ real numbers, $2g-1$ of which are the real moduli of $\Sigma$. The solutions have $2g+2$ asymptotic $AdS_5 \times S^5$ regions, $g$ three-spheres with RR 3-form charge, and another $g$ with NSNS 3-form charge. Collapse of consecutive branch points of $\Sigma $ yields singularities which correspond to D5 and NS5 branes in the probe limit. It is argued that the AdS/CFT dual gauge theory to each of our solutions consists of a 2+1-dimensional planar interface on which terminate $2g+2$ half-Minkowski 3+1-dimensional space-time $\mathcal{N}=4$ super-Yang-Mills theories. Generally, the $\\mathcal{N}=4$ theory in each Minkowski half-space-time may have an independent value of the gauge coupling, and the interface may support various operators, whose interface couplings are further free parameters of the dual gauge theory.