On 3-Dimensional Quantum Gravity and Quasi-Local Holography in Spin Foam Models and Group Field Theory

Schmid, Gabriel

doi:10.48550/arxiv.2205.05079

Cited by 1 publication

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“…(c) Note that the Theorem of Gagliardi-Ferri is not an "if-and-only-if " statement and there are also proper dipoles, which do not fall into the two classes defined above. See Appendix A.4 in [83] for a short discussion and examples. However, as it turns out, the two classes of proper dipole moves discussed in the Theorem of Gagliardi-Ferri are sufficient to characterize topological invariance, as stated in Theorem 2.15 below.…”

Section: Combinatorial and Topological Equivalencementioning

confidence: 99%

“…Afterwards, we will apply the techniques from crystallization theory discussed in the previous section, in order to rewrite the amplitudes as topological expansions similar in spirit to the topological expansion of the free energy in the large N limit proposed by R. Gurau [50][51][52]. The results of this section are based on the Master's thesis of one of the authors (GS) [83].…”

Section: Transition Amplitudesmentioning

confidence: 99%

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Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model

Goeller¹,

Oriti²,

Schmid³

2022

Preprint

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We consider transition amplitudes in the coloured simplicial Boulatov model for three-dimensional Riemannian quantum gravity. First, we discuss aspects of the topology of coloured graphs with non-empty boundaries. Using a modification of the standard rooting procedure of coloured tensor models, we then write transition amplitudes systematically as topological expansions. We analyse the transition amplitudes for the simplest boundary topology, the 2-sphere, and prove that they factorize into a sum entirely given by the combinatorics of the boundary spin network state and that the leading order is given by graphs representing the closed 3-ball in the large N limit. This is the first step towards a more detailed study of the holographic nature of coloured Boulatov-type GFT models for topological field theories and quantum gravity. Contents

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Section: Combinatorial and Topological Equivalencementioning

confidence: 99%