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

Abstract

Regularity and topology conditions are imposed on the exact Type IIB solutions on $Ad{S}_4\times S^2\times S^2\times \Sigma$ 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 $Ad{S}_5\times S^5$ (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 $Ad{S}_5\times S^5$. The genus $g\ge 1$ 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 $Ad{S}_5\times S^5$ 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 $mathcalN=4$ 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.

LaTeX, 64 pages, 10 figures

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