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A one-dimensional action for simplicial gravity in three dimensions



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Recording Details

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PIRSA Number: 
14030088

Abstract

Loop quantum gravity has a spinorial representation. Spinors simplify the symplectic structure of the theory, but can they also teach us something about the dynamics? We study this question in three dimensions, and derive the Ponzano–-Regge model from a spinorial action. Our construction starts from the first-order Palatini formalism, and gives the discretised action in the spinorial representation. A one-dimensional refinement limit brings us back to a continuum theory. The three-dimensional action turns into a line integral over the edges of the discretisation. We compute the gauge-fixed path integral for a generic simplicial discretisation. The resulting amplitudes reproduce the Ponzano–-Regge model.