Constructive Tensor Field Theory: The $${T_{4}^{4}}$$ T 4 4 Model
| Autor: | Fabien Vignes-Tourneret, Vincent Rivasseau |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Coupling constant
Rank (linear algebra) 010308 nuclear & particles physics Propagator Statistical and Nonlinear Physics 01 natural sciences Constructive Tensor field Quartic function 0103 physical sciences Four-tensor 010307 mathematical physics Laplace operator Mathematical Physics Mathematical physics Mathematics |
| Zdroj: | Communications in Mathematical Physics. 366:567-646 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-019-03369-9 |
| Popis: | We continue our constructive study of tensor field theory through the next natural model, namely the rank four tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on $U(1)^4$. This superrenormalizable tensor field theory has a power counting quite similar to ordinary $\phi^4_3$. We control the model via a multiscale loop vertex expansion which has to be pushed quite beyond the one of the $T^4_3$ model and we establish its Borel summability in the coupling constant. This paper is also a step to prepare the constructive treatment of just renormalizable models, such as the $T^4_5$ model with quartic melonic interactions. |
| Databáze: | OpenAIRE |
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