Abstract
In quantum gravity, we envision renormalization as the key tool for bridging the gap between microscopic models and observable scales. For spin foam quantum gravity, which is defined on a discretisation akin to lattice gauge theories, the goal is to derive an effective theory on a coarser discretisation from the dynamics on the finer one, coarse graining the system in the process and thus relating physics at different scales. In this review I will discuss the motivation for studying renormalization in spin foam quantum gravity, e.g. to restore diffeomorphism symmetry, and explain how to define renormalization in a background independent setting by formulating it in terms of boundary data. I will motivate the importance of the boundary data by studying coarse graining of a concrete example and extending this to the spin foam setting. This will naturally lead me to the methods currently used for renormalizing spin foam quantum gravity, such as tensor network renormalization, and a discussion of recent results. I will conclude with an overview of future prospects and research directions.
Highlights
A BRIEF INTRODUCTION TO SPIN FOAM QUANTUM GRAVITYSpin foam quantum gravity [1, 2] is a promising approach to quantum gravity closely related to loop quantum gravity [3]
Background Independence and the Interpretation ofScaleBefore we continue with reviewing how to coarse grain in practice, it is crucial to discuss the notion of “scale”—or the lack thereof
A well-understood result across models, which underlines the relation to general relativity, is the asymptotic expansion of the vertex amplitude dual to a 4-simplex [21,22,23,24,25]. In these works the vertex amplitude is investigated for coherent intertwiners, which are sharply peaked on the geometry of classical polyhedra
Summary
Spin foam quantum gravity [1, 2] is a promising approach to quantum gravity closely related to loop quantum gravity [3]. The starting point of spin foam models is the Plebanski-Holst formulation of general relativity [4], in which gravity is formulated as constrained topological BF theory [5] To formulate this theory as a path integral, one introduces a lattice as a regulator, more precisely a 2-complex, in order to truncate the number of degrees of freedom. A well-understood result across models, which underlines the relation to general relativity, is the asymptotic expansion of the vertex amplitude dual to a 4-simplex [21,22,23,24,25] In these works the vertex amplitude is investigated for coherent intertwiners, which are sharply peaked on the geometry of classical polyhedra.
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