Gauge Invariant Target Space Entanglement in D-Brane Holography

TL;DR

This paper develops a gauge-invariant framework for defining target space entanglement in D-brane holography, linking operator sub-algebras to bulk regions and providing calculable expressions for entanglement measures.

Contribution

It introduces a gauge-invariant method to characterize target space entanglement in D-brane theories using projection operators, advancing the understanding of bulk-boundary correspondence.

Findings

Provides a gauge-invariant characterization of target space entanglement.

Derives path integral expressions for Renyi entropies applicable to numerical analysis.

Connects operator sub-algebras to bulk regions via probe branes in the Coulomb branch.

Abstract

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.