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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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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
Renormalization of latticeregularized quantum gravity models I. General considerations
, 2014
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Quantum group spin nets: refinement
"... So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups SU(2)k and examine their effective continuum dynamics via tensor network renormalization. In the ..."
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So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups SU(2)k and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse graining procedure, we find a vast nontrivial fixed point structure beyond the degenerate and the BF phase. In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger’s construction principle [1] and the recent work [2], as the initial parametrization. In this new parametrization fine tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms. 1
1 The Tensor Track: an Update
, 2014
"... The tensor track approach to quantum gravity,1 is based on a new class of quantum field theories, hereafter called tensor group field theories (TGFTs).2–6 We provide a brief review of recent progress and list some desirable properties of TGFTs. In order to narrow the search for interesting models, w ..."
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The tensor track approach to quantum gravity,1 is based on a new class of quantum field theories, hereafter called tensor group field theories (TGFTs).2–6 We provide a brief review of recent progress and list some desirable properties of TGFTs. In order to narrow the search for interesting models, we also propose a set of guidelines for TGFT’s loosely inspired by the OsterwalderSchrader axioms of ordinary Euclidean QFT.