Road to Emergent Spacetime

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Examensarbete för masterexamen
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2019
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Nilsson, Torbjörn
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A long-standing issue in theoretical physics has been the difficulty of uniting Quantum Field Theory (QFT) and general relativity into a single theory of everything. There is ample evidence that reality is fundamentally quantum mechanical, and as such there should exist a quantum theory of gravity. Emergent spacetime is a novel approach to quantum gravity, wherein the usual method of starting with a classical theory and applying some kind of quantization recipe is reversed. Instead one begins with an abstract quantum theory and ’geometrizes’ it using recently discovered relationships between entanglement and geometry. This thesis is divided into three parts. The first part provides a comprehensive review of QFT, quantum information theory, string theory and how the AdS/CFT correspondence points towards an equivalence between spacetime connectivity and quantum entanglement. In the second part modern technical developments regarding the explicit emergence of spacetime from the entanglement structure of quantum states is reviewed. The main discovery that is reviewed is the explicit, fully controlled, emergence of second-order perturbative gravity with extra standard model fields from entanglement dynamics in conformal field theory. This result is then extended to include quantum corrections to the emergent gravitational theory by relating entanglement in the quantum theory to wormholes in the gravitational theory via the ER=EPR conjecture. The review is finished with an extension of the emergent spacetime program to discretized spacetimes, using the example of the AdS/MERA correspondence, which relates discretized anti-de Sitter to the MERA tensor network. In the third part some first steps towards the recovery of perturbative third-order gravitational dynamics from entanglement are carried out. The results show no inconsistencies, and the next step towards novel results is the characterization of the OPE between conformal primary scalars and the stress energy tensor in terms of symplectic forms in an auxiliary AdS space.
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