Weighting bubbles in group field theory
Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the bubbles of the graphs in the Feynman evaluations. In dimension thr...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
25 July 2014
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| In: |
Physical review. D, Particles, fields, gravitation, and cosmology
Year: 2014, Volume: 90, Issue: 2, Pages: 1-12 |
| ISSN: | 1550-2368 |
| DOI: | 10.1103/PhysRevD.90.024069 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevD.90.024069 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.90.024069 
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| Author Notes: | Aristide Baratin, Laurent Freidel and Razvan Gurau |
| Summary: | Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the bubbles of the graphs in the Feynman evaluations. In dimension three, our model exhibits new symmetries, interpreted as the action of the vertex translations of the triangulation. The extra field indices have an elegant algebraic interpretation: they encode the structure of a semisimple algebra. Remarkably, when the algebra is chosen to be associative, the new structure contributes a topological invariant from each bubble of the graph to the Feynman amplitudes. |
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| Item Description: | Gesehen am 05.10.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1550-2368 |
| DOI: | 10.1103/PhysRevD.90.024069 |