Zooming out of AdS$_4 \times$S$^2 \times$S$^2$: The Branes behind the CFT's

TL;DR

This paper identifies supersymmetric brane configurations underlying AdS4×S2×S2 supergravity solutions, elucidating their origin from branes in flat space and their relation to 3D N=4 CFTs and 4D N=4 SYM boundaries.

Contribution

It provides a detailed brane construction and geometric interpretation of AdS4×S2×S2 solutions, connecting weak-coupling brane configurations to supergravity regimes and explaining the Gaiotto-Witten classification.

Findings

Brane configurations preserve the same Killing spinors as flat space branes.

Singular sources correspond to semi-infinite D3-D5 and D3-NS5 spikes.

The AdS4 factor arises from universal self-similar brane bending regions.

Abstract

We reveal the supersymmetric brane configurations that give rise to AdS$_4\times$S$^2\times$S$^2$ 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 AdS$_4$ 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 AdS$_4\times$S$^2\times$S$^2$ solution.