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

TL;DR

This paper explores how certain 3D superconformal field theories can be used to recover the full Poincaré $AdS^5 imes S^5$ geometry in string theory duals by manipulating end-of-the-world branes, revealing new geometric configurations.

Contribution

It demonstrates that by choosing specific 3D SCFTs, the dual geometries can be extended to recover the complete Poincaré $AdS^5 imes S^5$ space, including wedge configurations with near $ heta= ext{pi}$ angles.

Findings

ETW branes can be pushed arbitrarily far, recovering the full $AdS^5 imes S^5$.

Existence of 3D SCFTs with dual wedges of $AdS^5 imes S^5$ with angles close to $ heta= ext{pi}$.

Geometric configurations include end-of-the-world branes on either side of the wedge.

Abstract

We study solutions of type IIB string theory dual to ${\cal N}=4$ 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 $AdS^5 \times S^5$ 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 Poincar\'e $AdS^5 \times S^5$. 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 Poincar\'e $AdS^5 \times S^5$. We also show that there are 3D SCFTs whose dual includes a wedge of Poincar\'e $AdS^5 \times S^5$ with an angle arbitrarily close to $\pi$, with geometrical ETW branes on either side.