  A construction of a gravity dual to a physical gauge theory requires
confronting data. We establish a proof-of-concept for precision holography,
i.e., the explicit reconstruction of the dual background metric functions
directly from the entanglement entropy (EE) of strip subregions that we extract
from pure glue Yang-Mills theory discretized on a lattice. Our main focus is on
a three-dimensional Euclidean SU(2) theory in the deconfining phase.
Holographic EE suggests, and we find evidence for, that the scaling of the
thermal entropy with temperature is to power 7/3 and that it approaches
smoothly the critical point, consistent with black hole thermodynamics. In
addition, we provide frugal results on the potential between quenched quarks by
the computation of the Polyakov loop correlators on the lattice. Holographic
arguments pique curiosity in the substratum of Debye screening at strong
coupling.
