Quantum field theories with many fields
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911485841637376 |
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| author | Fraser-Taliente, Ludo |
| author_facet | Fraser-Taliente, Ludo |
| contents | The large-$N$ quantum field theories provide a window into the regime of strongly-coupled physics. Our principal object of study in this thesis is the large-$N$ family of melonic QFTs, which contain the Sachdev-Ye-Kitaev-like models, tensor models, and vector models. We begin with a review of this limit of a large number of degrees of freedom (large-$N$) as an approach to the solution of QFTs. Two toy models are used to clarify this approach: a zero-dimensional field theory and the flow of a generalized free field theory. Both models are solvable, and so we can explicitly demonstrate: using the former, the simplifications at large $N$; using the latter, the tools used to study scale-dependence of physics -- the renormalization group. We develop $\tilde{F}$-extremization, a simple method of solution for an arbitrary large-$N$ melonic QFT in its strongly-coupled limit. The infrared conformal field theories show remarkable simplicity, in that they are entirely solved by the requirement that they have as many degrees of freedom as possible, up to a simple constraint arising from the interaction between the fields. We measure the number of degrees of freedom of the conformal infrared theory via $\tilde{F}$, the universal part of the free energy. We then present the example of the quartic Yukawa model in continuous dimension. This model is considered as a tensor field theory, and solved for its conformal limit; we then illustrate its multiplicity of fixed points and their stability, as well as its operator spectrum, matching the data between the large-$N$ and dimensional expansions. These features reflect general characteristics of melonic conformal field theories: their existence, stability, and spectral characteristics. We conclude with future directions of exploration for the melonic theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04481 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum field theories with many fields Fraser-Taliente, Ludo High Energy Physics - Theory The large-$N$ quantum field theories provide a window into the regime of strongly-coupled physics. Our principal object of study in this thesis is the large-$N$ family of melonic QFTs, which contain the Sachdev-Ye-Kitaev-like models, tensor models, and vector models. We begin with a review of this limit of a large number of degrees of freedom (large-$N$) as an approach to the solution of QFTs. Two toy models are used to clarify this approach: a zero-dimensional field theory and the flow of a generalized free field theory. Both models are solvable, and so we can explicitly demonstrate: using the former, the simplifications at large $N$; using the latter, the tools used to study scale-dependence of physics -- the renormalization group. We develop $\tilde{F}$-extremization, a simple method of solution for an arbitrary large-$N$ melonic QFT in its strongly-coupled limit. The infrared conformal field theories show remarkable simplicity, in that they are entirely solved by the requirement that they have as many degrees of freedom as possible, up to a simple constraint arising from the interaction between the fields. We measure the number of degrees of freedom of the conformal infrared theory via $\tilde{F}$, the universal part of the free energy. We then present the example of the quartic Yukawa model in continuous dimension. This model is considered as a tensor field theory, and solved for its conformal limit; we then illustrate its multiplicity of fixed points and their stability, as well as its operator spectrum, matching the data between the large-$N$ and dimensional expansions. These features reflect general characteristics of melonic conformal field theories: their existence, stability, and spectral characteristics. We conclude with future directions of exploration for the melonic theories. |
| title | Quantum field theories with many fields |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.04481 |