Zooming out of AdS4 ×S2 ×S2: The Branes behind the CFT's
Abstract
We reveal the supersymmetric brane configurations that give rise to AdS4×S2×S2 supergravity solutions, which are holographic duals to three-dimensional N=4 CFTs or to conformal boundaries and domain walls of four-dimensional N=4 SYM. We show that these solutions preserve the same Killing spinors as orthogonal D3, D5 and NS5 branes in flat space, and that the singular sources of these solutions correspond to semi-infinite D3-D5 and D3-NS5 spikes. We track these solutions all the way from the weak-coupling regime of parameters, where the branes do not backreact, to the supergravity regime. We explain how the AdS4 factor arises from certain universal self-similar bending regions of the five-branes, whose steepness is the same as the weak-coupling linking numbers. We also propose a brane configuration that gives rise to the Janus interface solutions. Our construction gives a clear geometric explanation of the Gaiotto-Witten "good-bad-ugly" classification of eight-supercharge theories: only good theories have five-branes that do not cross when back-reacting, and end up sourcing an AdS4×S2×S2 solution.
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