Conformal Invariance of the large-$N$ limit of the $O(N)$ universality class
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911626803806208 |
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| author | Cabrera, Santiago De Polsi, Gonzalo Rançon, Adam Wschebor, Nicolás |
| author_facet | Cabrera, Santiago De Polsi, Gonzalo Rançon, Adam Wschebor, Nicolás |
| contents | Conformal symmetry is expected to be realized in many equilibrium statistical mechanical systems at criticality. Although this is certainly true in two-dimensional systems, the three-dimensional case is subtler, and only a few proofs exist, only so in very specific cases. In this work, we give two proofs for the large $N$ limit of the $O(N)$ universality class within the non-perturbative renormalization group framework: one functional, and one vertex-by-vertex in Fourier space. While doing so, we unveil how the theory is structured in order for conformal symmetry to be realized. As a consequence, we shed light on what to expect, on rather general grounds, for a theory to be conformally invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24675 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conformal Invariance of the large-$N$ limit of the $O(N)$ universality class Cabrera, Santiago De Polsi, Gonzalo Rançon, Adam Wschebor, Nicolás Statistical Mechanics High Energy Physics - Theory Conformal symmetry is expected to be realized in many equilibrium statistical mechanical systems at criticality. Although this is certainly true in two-dimensional systems, the three-dimensional case is subtler, and only a few proofs exist, only so in very specific cases. In this work, we give two proofs for the large $N$ limit of the $O(N)$ universality class within the non-perturbative renormalization group framework: one functional, and one vertex-by-vertex in Fourier space. While doing so, we unveil how the theory is structured in order for conformal symmetry to be realized. As a consequence, we shed light on what to expect, on rather general grounds, for a theory to be conformally invariant. |
| title | Conformal Invariance of the large-$N$ limit of the $O(N)$ universality class |
| topic | Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.24675 |