Abstract
This work is meant as a review summary of a series of recent results concerning the derivation of a holographic entanglement entropy formula for generic open spin network states in the group field theory (GFT) approach to quantum gravity. The statistical group-field computation of the Rényi entropy for a bipartite network state for a simple interacting GFT is reviewed, within a recently proposed dictionary between group field theories and random tensor networks, and with an emphasis on the problem of a consistent characterisation of the entanglement entropy in the GFT second quantisation formalism.
Highlights
Two potentially revolutionary ideas have inspired much work in contemporary theoretical physics.Both ideas herald from the use of the general information theoretic approach to the problem of quantum gravity
In loop quantum gravity (LQG), such theories play the role of auxiliary field theories, whose partition functions, for appropriate choices of the kernels, provide generating functionals for the Loop Quantum Gravity (LQG) spinfoams: a covariant path integral realisation of spacetime as a transition amplitude between boundary spin network states
group field theory (GFT) provide a versatile field-theoretic tool to study the very emergence of space-time quantum geometry via path integral techniques and a quantum many-body approach associated with their second quantised formalism [57,63]
Summary
Two potentially revolutionary ideas have inspired much work in contemporary theoretical physics. More than that, differently from the semiclassical framework, in the non-perturbative scheme, holography as detected in gravitational systems, as well as any macroscopic feature of our geometric universe, would result from purely quantum properties of the microscopic constituents of spacetime, but they can— only—be understood in this light This perspective is manifest in the Group Field Theory (GFT) formalism, a promising convergence of the insights and results from matrix models [44,45], loop quantum gravity and simplicial approaches into a background independent quantum field theory setup. As a higher order generalisation of matrix models, the GFT formalism at the same time provides a field-theoretic and inherently covariant framework for generalising the tensor networks approach to the holographic aspects of quantum many-body systems in condensed matter and in the AdS/CFT context This makes GFT a very effective framework to investigate how space-time geometry, together with its holographic behaviour and macroscopic dynamics, arise from entanglement between the fundamental constituents. A brief discussion and an appendix on the notion of coherent states over-completeness close the manuscript
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