Loop quantum gravity boundary dynamics and SL(2,C) gauge theory
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Publication:5163552
DOI10.1088/1361-6382/AC03F8zbMATH Open1481.83045arXiv2101.07565OpenAlexW3164544042MaRDI QIDQ5163552
Author name not available (Why is that?)
Publication date: 4 November 2021
Published in: (Search for Journal in Brave)
Abstract: In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3+1 space-time dimensions, the boundary theory lives on the 2+1-dimensional time-like boundary and is supposed to describe the time evolution of the edge modes living on the 2-dimensional boundary of space, i.e. the space-time corner. Focusing on "electric" excitations -- quanta of area -- living on the corner, we formulate their dynamics in terms of classical spinor variables and we show that the coupling constants of a polynomial Hamiltonian can be understood as the components of a background boundary 2+1-metric. This leads to a deeper conjecture of a correspondence between boundary Hamiltonian and boundary metric states. We further show that one can reformulate the quanta of area data in terms of a SL(2,C) connection, transporting the spinors on the boundary surface and whose SU(2) component would define "magnetic" excitations (tangential Ashtekar-Barbero connection), thereby opening the door to writing the loop quantum gravity boundary dynamics as a 2+1-dimensional SL(2,C) gauge theory.
Full work available at URL: https://arxiv.org/abs/2101.07565
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