Finding $Ad{S}^5\times S^5$ in 2+1 dimensional SCFT physics

Abstract

We study solutions of type IIB string theory dual to $\mathcal{N}=4$ supersymmetric Yang-Mills theory on half of ${\mathbb{R}}^{3,1}$ coupled to holographic three-dimensional superconformal field theories (SCFTs) at the edge of this half-space. The dual geometries are asymptotically $Ad{S}^5\times S^5$ with boundary geometry ${\mathbb{R}}^{2,1}\times {\mathbb{R}}^{+}$, with a geometrical end-of-the-world (ETW) brane cutting off the other half of the asymptotic region of the would-be Poincaré $Ad{S}^5\times S^5$. We show that by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily far towards the missing asymptotic region, recovering the "missing" half of Poincaré $Ad{S}^5\times S^5$. We also show that there are 3D SCFTs whose dual includes a wedge of Poincaré $Ad{S}^5\times S^5$ with an angle arbitrarily close to $\pi$, with geometrical ETW branes on either side.

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