Sextic tensor model in rank 3 at next-to-leading order
We compute the four-loop beta functions of short and long-range multi scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a $U(N)^3$ symmetry and study the renormalization group at next-to-leading order in $N$ and small $\epsilon$. In the short...
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| Main Author: | |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
16 Sep 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-23 |
| DOI: | 10.48550/arXiv.2109.08034 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2109.08034 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2109.08034 
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| Author Notes: | Sabine Harribey |
| Summary: | We compute the four-loop beta functions of short and long-range multi scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a $U(N)^3$ symmetry and study the renormalization group at next-to-leading order in $N$ and small $\epsilon$. In the short-range case, $\epsilon$ is the deviation from the critical dimension while it is the deviation from the critical scaling of the free propagator in the long-range case. This allows us to find the $1/N$ corrections to the rank-3 sextic tensor model of arXiv:1912.06641. In the short-range case, we still find a non-trivial real IR stable fixed point, with a diagonalizable stability matrix. All couplings, except for the so-called wheel coupling, have terms of order $\epsilon^0$ at leading and next-to-leading order, which makes this fixed point different from the other melonic fixed points found in quartic models. In the long-range case, the corrections to the fixed point are instead not perturbative in $\epsilon$ and hence unreliable; we thus find no precursor of the large-$N$ fixed point. |
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| Item Description: | Gesehen am 28.09.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2109.08034 |