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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2012-04-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.020 |
| _version_ | 1819154855525089280 |
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| author | Razvan Gurau James P. Ryan |
| author_facet | Razvan Gurau James P. Ryan |
| author_sort | Razvan Gurau |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-22T15:27:43Z |
| format | Article |
| id | doaj.art-62708b0802004c6cb364344488e89411 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-22T15:27:43Z |
| publishDate | 2012-04-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-62708b0802004c6cb364344488e894112022-12-21T18:21:27ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-04-018020Colored Tensor Models - a ReviewRazvan GurauJames P. RyanColored 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.http://dx.doi.org/10.3842/SIGMA.2012.020colored tensor models1/N expansion |
| spellingShingle | Razvan Gurau James P. Ryan Colored Tensor Models - a Review Symmetry, Integrability and Geometry: Methods and Applications colored tensor models 1/N expansion |
| title | 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_short | Colored Tensor Models - a Review |
| title_sort | colored tensor models a review |
| topic | colored tensor models 1/N expansion |
| url | http://dx.doi.org/10.3842/SIGMA.2012.020 |
| work_keys_str_mv | AT razvangurau coloredtensormodelsareview AT jamespryan coloredtensormodelsareview |