Abstract
We couple to group field theory (GFT) a scalar field that encodes the entanglement between manifold sites. The scalar field provides a relational clock that enables the derivation of the Hamiltonian of the system from the GFT action. Inspecting the Hamiltonian, we show that a theory of emergent gravity arises, and that this can be recast according to the Ashtekar’s formulation of general relativity. The evolution of the GFT observables is regulated by the Shrödinger equation generated by the Hamiltonian. This is achieved by imposing a renormalization group (RG) flow that corresponds to a simplified Ricci flow. As a consequence of the quantization procedure, the Hamiltonian is recovered to be non-Hermitian, and can be related to the complex action formalism, in which the initial conditions and the related future evolution of the systems are dictated by the imaginary part of the action.
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Acknowledgments
The authors thank Steffen Gielen, Ling-Yan Hung, Simon Langenscheidt, Luca Marchetti, Daniele Oriti, and Edward Wilson-Ewing for valuable discussions. The work of S.A. is supported in part by the Simons Foundation award number 896696. A.M. wishes to acknowledge support by the Shanghai Municipality, through the grant No. KBH1512299, by Fudan University, through the grant No. JJH1512105, the Natural Science Foundation of China, through the grant No. 11875113, and by the Department of Physics at Fudan University, through the grant No. IDH1512092/001. R.P. is supported in part by the Swedish Research Council grant, contract number 2016-05996, as well as by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 668679).
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Liu, J., Alexander, S., Marcianò, A. et al. A path integral formula of quantum gravity emergent from entangled local structures. J. High Energ. Phys. 2024, 219 (2024). https://doi.org/10.1007/JHEP07(2024)219
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DOI: https://doi.org/10.1007/JHEP07(2024)219