Loop Quantum Gravity's Boundary Maps

Abstract

In canonical quantum gravity, the presence of spatial boundaries naturally leads to a boundary quantum states, representing quantum boundary conditions for the bulk fields. As a consequence, quantum states of the bulk geometry needs to be upgraded to wave-functions valued in the boundary Hilbert space: the bulk become quantum operator acting on boundary states. We apply this to loop quantum gravity and describe spin networks with 2d boundary as wave-functions mapping bulk holonomies to spin states on the boundary. This sets the bulk-boundary relation in a clear mathematical framework, which allows to define the boundary density matrix induced by a bulk spin network states after tracing out the bulk degrees of freedom. We ask the question of the bulk reconstruction and prove a boundary-to-bulk universal reconstruction procedure, to be understood as a purification of the mixed boundary state into a pure bulk state. We further perform a first investigation in the algebraic structure of induced boundary density matrices and show how correlations between bulk excitations, i.e. quanta of 3d geometry, get reflected into the boundary density matrix.

23 pages

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Cited by in corpus (8)

• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Holographic maps from quantum gravity states as tensor networks
• Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
• Holographic entanglement in spin network states: a focused review
• Loop Quantum Gravity and Quantum Information
• Intertwiner Entanglement Excitation and Holonomy Operator
• Curvature from multipartite entanglement in quantum gravity states
• The Ponzano-Regge cylinder and Propagator for 3d quantum gravity