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19
Emergent Models for Gravity: an Overview of Microscopic Models
, 2012
"... We give a critical overview of various attempts to describe gravity as an emergent phenomenon, starting from examples of condensed matter physics, to arrive to more sophisticated pregeometric models. The common line of thought is to view the graviton as a composite particle/collective mode. Howeve ..."
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Cited by 8 (1 self)
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We give a critical overview of various attempts to describe gravity as an emergent phenomenon, starting from examples of condensed matter physics, to arrive to more sophisticated pregeometric models. The common line of thought is to view the graviton as a composite particle/collective mode. However, we will describe many different ways in which this idea is realized in practice.
Coarse graining of spin net models: dynamics of intertwiners
- New J. Phys
"... Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full four–dimensional models. We consider here simplified analogue models, so ..."
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Cited by 4 (3 self)
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Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full four–dimensional models. We consider here simplified analogue models, so called spin nets, that retain the main dynamical ingredient of spin foams, the simplicity constraints. For a certain class of these spin net models we determine the phase diagram and therefore the continuum phases via a coarse graining procedure based on tensor network renormalization. This procedure will also reveal an unexpected fixed point, which turns out to define a new triangulation invariant vertex model. 1
Topological lattice field theories from intertwiner dynamics,” arXiv:1311.1798 [gr-qc
"... We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models gi ..."
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Cited by 3 (3 self)
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We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models. 1
Renormalization of lattice-regularized quantum gravity models I. General considerations
, 2014
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Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
"... We study a just-renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the mo ..."
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We study a just-renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.
