Colored Tensor Models - a Review
Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have...
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| Date: | 2012 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148407 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Colored Tensor Models - a Review / R. Gurau, J.P. Ryan // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 130 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1484072019-02-19T01:30:04Z Colored Tensor Models - a Review Gurau, R. Ryan, J.P. Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions), non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions. 2012 Article Colored Tensor Models - a Review / R. Gurau, J.P. Ryan // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 130 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05C15; 05C75; 81Q30; 81T17; 81T18; 83C27; 83C45 DOI: http://dx.doi.org/10.3842/SIGMA.2012.020 http://dspace.nbuv.gov.ua/handle/123456789/148407 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions), non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions. |
| format |
Article |
| author |
Gurau, R. Ryan, J.P. |
| spellingShingle |
Gurau, R. Ryan, J.P. Colored Tensor Models - a Review Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Gurau, R. Ryan, J.P. |
| author_sort |
Gurau, R. |
| title |
Colored Tensor Models - a Review |
| title_short |
Colored Tensor Models - a Review |
| title_full |
Colored Tensor Models - a Review |
| title_fullStr |
Colored Tensor Models - a Review |
| title_full_unstemmed |
Colored Tensor Models - a Review |
| title_sort |
colored tensor models - a review |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148407 |
| citation_txt |
Colored Tensor Models - a Review / R. Gurau, J.P. Ryan // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 130 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT guraur coloredtensormodelsareview AT ryanjp coloredtensormodelsareview |
| first_indexed |
2025-07-12T19:23:23Z |
| last_indexed |
2025-07-12T19:23:23Z |
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1837470270403641344 |