  It has been suggested in arXiv:2004.00613 that in Dp-brane holography,
entanglement in the target space of the D-brane Yang-Mills theory provides a
precise notion of bulk entanglement in the gravity dual. We expand on this
discussion by providing a gauge invariant characterization of operator
sub-algebras corresponding to such entanglement. This is achieved by finding a
projection operator which imposes a constraint characterizing the target space
region of interest. By considering probe branes in the Coulomb branch we
provide motivation for why the operator sub-algebras we consider are
appropriate for describing a class of measurements carried out with low-energy
probes in the corresponding bulk region of interest. We derive expressions for
the corresponding Renyi entropies in terms of path integrals which can be
directly used in numerical calculations.

High Energy Physics - Theory;Statistical Mechanics;Quantum Physics