Towards precision holography

A minimal requirement for any strongly coupled gauge field theory to have a classical dual bulk gravity description is that one should in principle be able to recover the full geometry as encoded on the asymptotics of the spacetime. Even this requirement cannot be fulfilled with arbitrary precision simply due to the fact that the boundary data is inherently noisy. We present a statistical approach to bulk reconstruction from entanglement entropy measurements, which handles the presence of noise in a natural way. Our approach therefore opens up a novel gateway for precision holography.

Figure 1

Left: generated data points (black). The error bars denote the 95% central confidence interval (CCI) of individual points. The red dashed curve denotes the exact entanglement entropy computed with (16). Right: sampled metric data (black). The solid black curve denotes the median value of the metric. The gray and light gray curves correspond to 50% and 95% CCIs, respectively.

Figure 2

In all panels the black curve corresponds to the median value and the gray/light gray curves correspond to 50%/95% CCIs. The red dashed curve is the value computed using (16). Left: two-point function. Middle: quark-antiquark potential for temporal Wilson loop. Right: same for the spatial Wilson loop.