The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other hand, the core of the paper is to establish results about the topological and geometrical properties of the Gurau-degree (or G-degree) of the represented manifolds, in relation with the motivations coming from physics. In fact, the G-degree appears naturally in higher dimensional tensor models as the quantity driving their 1/N expansion, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting. In particular, the G-degree of PL-manifolds is proved to be finite-to-one in any dimension, while in dimension 3 and 4 a series of classification theorems are obtained for PL-manifolds represented by graphs with a fixed G-degree. All these properties have specific relevance in the tensor models framework, showing a direct fruitful interaction between tensor models and discrete geometry, via crystallization theory.
Topology in colored tensor models via crystallization theory / Casali, Maria Rita; Cristofori, Paola; Dartois, Stèphane; Grasselli, Luigi. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 129(2018), pp. 142-167.
Data di pubblicazione: | 2018 |
Data di prima pubblicazione: | 8-gen-2018 |
Titolo: | Topology in colored tensor models via crystallization theory |
Autore/i: | Casali, Maria Rita; Cristofori, Paola; Dartois, Stèphane; Grasselli, Luigi |
Autore/i UNIMORE: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.geomphys.2018.01.001 |
Rivista: | |
Volume: | 129 |
Pagina iniziale: | 142 |
Pagina finale: | 167 |
Codice identificativo ISI: | WOS:000432095800011 |
Codice identificativo Scopus: | 2-s2.0-85044480521 |
Citazione: | Topology in colored tensor models via crystallization theory / Casali, Maria Rita; Cristofori, Paola; Dartois, Stèphane; Grasselli, Luigi. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 129(2018), pp. 142-167. |
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