Target Space Entanglement Entropy

Abstract

We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen sub-algebra of observables $\mathcal{A}$. The entanglement entropy is calculated as the entropy of the density matrix restricted to $\mathcal{A}$. As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra $\mathcal{A}$ is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting.

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Cited by in corpus (13)

• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Bulk geometry in gauge/gravity duality and color degrees of freedom
• Target space entanglement in Matrix Models
• Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces
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• Towards a unitary formulation of quantum field theory in curved spacetime: the case of de Sitter spacetime
• Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics
• Fiducial observers and the thermal atmosphere in the black hole quantum throat